Step 1: Understanding the Concept:

Equilibrium refers to a state where the net external force acting on a body is zero.

Dynamic equilibrium occurs when a body remains in a state of uniform motion (constant velocity) in a straight line.


Step 2: Detailed Explanation:

According to Newton's Second Law of Motion, \( F_{net} = m \cdot a \).

For a body to be in equilibrium (static or dynamic), the net force \( F_{net} \) must be zero.

If \( F_{net} = 0 \), then the acceleration \( a \) must also be zero.

In dynamic equilibrium, the body has a non-zero constant velocity \( v \), which implies its change in velocity over time is zero, hence \( a = 0 \).


Step 3: Final Answer:

Therefore, for dynamic equilibrium, the acceleration of the body must be zero.
Quick Tip: Remember: Static Equilibrium means Velocity = 0 and Acceleration = 0. Dynamic Equilibrium means Velocity = Constant (\(\neq\) 0) and Acceleration = 0.

Step 1: Understanding the Concept:

Photosynthesis is the biological process by which green plants convert raw materials like carbon dioxide and water into glucose.


Step 2: Detailed Explanation:

During photosynthesis, chlorophyll in the leaves captures solar energy (light energy) from the sun.

This light energy is used to trigger chemical reactions that store energy in the chemical bonds of glucose (chemical energy).

The process is summarized as:
\[ 6CO_2 + 6H_2O + Light Energy \rightarrow C_6H_{12}O_6 + 6O_2 \]


Step 3: Final Answer:

The transformation is light energy to chemical energy.
Quick Tip: Think of plants as solar panels that store the sun's energy in "food batteries" (chemical bonds).

Step 1: Understanding the Concept:

In a block and tackle system, the Velocity Ratio (VR) is determined by the number of strands of the string supporting the movable block.


Step 2: Key Formula or Approach:

If the effort is applied in the downward direction, \( VR = n \) (where \( n \) is the number of pulleys).

If the effort is applied in the upward direction, the effort strand itself contributes to lifting the load, so \( VR = n + 1 \).


Step 3: Detailed Explanation:

The system has \( n = 3 \) pulleys.

The effort is applied in the upward direction.

Therefore, \( VR = 3 + 1 = 4 \).


Step 4: Final Answer:

The Velocity Ratio is 4.
Quick Tip: If the free end of the string comes out of the lower (movable) block, the VR is always \( n + 1 \).

Step 1: Understanding the Concept:

According to Snell's Law, the refractive index of the second medium with respect to the first medium is the ratio of the sine of the angle of incidence to the sine of the angle of refraction.

Critical Note: The angles must be measured between the ray and the normal.


Step 2: Key Formula or Approach:
\[ _A\mu_B = \frac{\sin i}{\sin r} \]


Step 3: Detailed Explanation:

From the diagram, the angle between the incident ray and the interface in Medium A is \( 45^\circ \).

The normal \( NN' \) is perpendicular to the interface.

Angle of incidence \( i = 90^\circ - 45^\circ = 45^\circ \).

In Medium B, the angle between the refracted ray and the interface is \( 30^\circ \).

Angle of refraction \( r = 90^\circ - 30^\circ = 60^\circ \).

Substituting into the formula:
\[ _A\mu_B = \frac{\sin 45^\circ}{\sin 60^\circ} \]


Step 4: Final Answer:

The correct expression is \( \frac{\sin 45^\circ}{\sin 60^\circ} \).
Quick Tip: Don't be tricked by the diagram! Always check if the angle is given with the surface or the normal. \( Angle_{Normal} = 90^\circ - Angle_{Surface} \).

Step 1: Understanding the Concept:

The solar spectrum consists of visible light and invisible radiations. The region just beyond the red end of visible light is the infrared region.


Step 2: Detailed Explanation:

Infrared radiations are thermal radiations. They have high heating power because their frequencies match the vibrational frequencies of many molecules.

A blackened bulb absorbs these radiations efficiently, leading to a significant increase in temperature.

This property was used by William Herschel to discover infrared rays.


Step 3: Final Answer:

The heating effect beyond the red region is caused by infrared radiations.
Quick Tip: Infrared = Heat rays. Ultraviolet = Chemical/Fluorescence rays.

Step 1: Understanding the Concept:

Mechanical energy is the sum of kinetic energy (\( K \)) and potential energy (\( U \)).


Step 2: Key Formula or Approach:

Total Mechanical Energy \( E = K + U \).


Step 3: Detailed Explanation:

The problem states "assuming no loss of energy," which means there is no friction or air resistance (conservative system).

As the cyclist moves up the hill, his velocity decreases (kinetic energy decreases) and his height increases (gravitational potential energy increases).

According to the Law of Conservation of Energy, the energy is merely transformed from kinetic to potential, but the total sum \( E \) stays the same.


Step 4: Final Answer:

The total mechanical energy remains constant.
Quick Tip: In the absence of dissipative forces like friction, mechanical energy is always conserved.

Step 1: Understanding the Concept:

This question pertains to the characteristics of images formed by a concave lens.


Step 2: Detailed Explanation:

A concave lens always produces a virtual, erect, and diminished image for any position of the real object.

The image is always formed between the optical center (\( O \)) and the focus (\( F \)) on the same side as the object.

Therefore, the magnitude of the image distance \( v \) is always less than or equal to the focal length \( f \).

Given \( f = 15 cm \), the image distance \( v \leq 15 cm \).


Step 3: Final Answer:

The value is less than or equal to 15 cm.
Quick Tip: For a concave lens, the virtual image is restricted to the region between the lens and the focus.

Step 1: Understanding the Concept:

Rayleigh scattering explains why the sky is blue, while the refractive index explains how light bends in a medium.


Step 2: Detailed Explanation:

Assertion (A): Rayleigh's Law of Scattering states that the intensity of scattered light is inversely proportional to the fourth power of the wavelength (\( I \propto 1/\lambda^4 \)). Since blue light has a shorter wavelength than red light, it is scattered more. (A is true).

Reason (R): Cauchy's formula states that refractive index \( \mu \) increases as wavelength decreases. Thus, \( \mu_{blue} > \mu_{red} \). (R is true).

However, scattering is caused by the interaction of light with particles much smaller than its wavelength, whereas refractive index describes the phase velocity of light in a bulk medium. The reason for scattering is the small wavelength, not the high refractive index.


Step 3: Final Answer:

Both statements are correct, but R does not explain why A happens.
Quick Tip: Scattering is a diffraction-like phenomenon at the particle level. Refraction is a bulk property of the medium.

Step 1: Understanding the Concept:

In a circuit, components in series share the same current path. If one fails, the circuit breaks. Components in parallel have independent current paths.


Step 2: Detailed Explanation:

Looking at the diagram:
\( L_1 \) is in series with the entire combination. If it fails, the whole circuit opens.
\( L_2, L_3, \) and \( L_4 \) are in parallel branches.

If \( L_4 \) fails, the branch containing \( L_4 \) becomes an open circuit. However, current can still flow from the battery through \( L_1 \) and then through the other parallel branches (\( L_2 \) and \( L_3 \)).

Thus, \( L_4 \) (as a parallel component) does not stop the flow to others.


Step 3: Final Answer:

The correct lamp is \( L_4 \).
Quick Tip: Parallel = Independent paths. Series = Dependent path.

Step 1: Understanding the Concept:

Shrillness is another term for high pitch or high frequency. For an air column in a pipe, the frequency is inversely proportional to the length of the air column (\( f \propto 1/L \)).


Step 2: Detailed Explanation:

Volume of water \( V \) is constant. \( V = \pi r^2 h \), where \( h \) is the height of water.

Since \( r_A \) is the smallest, the height of water \( h_A \) will be the greatest (\( h = V / \pi r^2 \)).

Length of the air column \( L = Height of Jar - Height of Water \).

Jar A, having the most water, will have the shortest air column.

Since Jar A has the shortest air column, it produces the highest frequency (shrillest note).


Step 3: Final Answer:

Jar A produces the shrillest note.
Quick Tip: Shortest air column = Highest frequency = Shriller sound. Think of a flute or test tubes with different water levels.

Step 1: Understanding the Concept:

Specific heat capacity is the amount of heat required to raise the temperature of unit mass of a substance by 1 degree Celsius.


Step 2: Detailed Explanation:

Specific heat capacity is a characteristic property of a material. It depends only on the nature of the substance and its state of matter.

Stretching a wire changes its physical dimensions (length and area) but does not change the material it is made of.

Because the material is the same, the specific heat capacity remains unchanged.


Step 3: Final Answer:

The specific heat capacity remains the same.
Quick Tip: Be careful! Resistance would change (becomes 4 times), but characteristic properties like resistivity and specific heat capacity do not change with dimensions.

Step 1: Understanding the Concept:

The reciprocal of the equivalent resistance of a parallel combination is the sum of the reciprocals of the individual resistances.


Step 2: Key Formula or Approach:
\[ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} \]


Step 3: Detailed Explanation:

Taking the LCM on the right side:
\[ \frac{1}{R_p} = \frac{R_2 + R_1}{R_1 \cdot R_2} \]

To find \( R_p \), take the reciprocal of the whole expression:
\[ R_p = \frac{R_1 R_2}{R_1 + R_2} \]


Step 4: Final Answer:

The equivalent resistance is the product of the two resistances divided by their sum.
Quick Tip: Mnemonic for 2 resistors in parallel: "Product over Sum".

Step 1: Understanding the Concept:

The Right-Hand Thumb Rule determines the direction of the magnetic field around a straight conductor.


Step 2: Key Formula or Approach:

Thumb = Direction of current. Fingers = Direction of magnetic field lines.


Step 3: Detailed Explanation:

The cross (X) indicates that the current is flowing into the paper.

Using the Right-Hand Thumb Rule, point your thumb into the page. Your fingers curl in a clockwise direction.

The magnetic field lines are circles centered on the wire.

At position 1 (Top), the clockwise tangent points to the right. Compass 1 shows this direction. (Aligned).

At position 2 (Right), the clockwise tangent points downwards. Compass 2 shows an upward direction. (Not aligned).


Step 4: Final Answer:

Only compass 1 is correctly aligned.
Quick Tip: X = Into page = Clockwise. Dot (.) = Out of page = Anti-clockwise.

Step 1: Understanding the Concept:

Latent heat of fusion (\( L \)) is the heat required to change a substance from solid to liquid without changing its temperature.


Step 2: Key Formula or Approach:
\[ Q = m \cdot L \]

Since heat is absorbed at a constant rate (\( P \)), total heat \( Q = P \cdot t \).


Step 3: Detailed Explanation:

Combining the formulas: \( m \cdot L = P \cdot t \).

Since mass (\( m \)) and power (\( P \)) are the same for all three:
\[ L \propto t \]

The substance that takes more time to melt completely requires more total heat, implying it has a higher specific latent heat.

Substance B takes the longest time (7 minutes).


Step 4: Final Answer:

Substance B has the highest specific latent heat.
Quick Tip: More time taken to melt (at the same heating rate) = More heat energy required = Higher Latent Heat.

Step 1: Understanding the Concept:

The mass number of an atom is defined as the total number of nucleons (protons + neutrons) in the nucleus.


Step 2: Key Formula or Approach:
\[ Mass Number (A) = Number of Protons (Z) + Number of Neutrons (N) \]


Step 3: Detailed Explanation:

Given:

Protons = 3

Neutrons = 4

Electrons = 3 (Electrons are not counted in the mass number because their mass is negligible).
\[ A = 3 + 4 = 7 \]


Step 4: Final Answer:

The mass number is 7.
Quick Tip: Atomic number = Protons. Mass number = Sum of heavy particles in the nucleus.

Step 1: Understanding the Concept:

According to Snell's Law, the refractive index of glass with respect to air (\( _{a}\mu_{g} \)) is the ratio of the sine of the angle of incidence in air to the sine of the angle of refraction in glass.


Step 2: Key Formula or Approach:

Refractive index of glass with respect to air: \( _{a}\mu_{g} = \frac{\sin i_{1}}{\sin r_{1}} \)

Refractive index of air with respect to glass: \( _{g}\mu_{a} = \frac{\sin i_{2}}{\sin r_{2}} \)

By the Principle of Reversibility: \( _{a}\mu_{g} \times _{g}\mu_{a} = 1 \)


Step 3: Detailed Explanation:

At the first surface, the ratio \( \frac{\sin i}{\sin r} \) is equal to \( _{a}\mu_{g} \).

At the second surface, the ray travels from glass to air, so the ratio \( \frac{\sin i}{\sin r} \) is equal to \( _{g}\mu_{a} \).

The product of these two ratios is:
\[ _{a}\mu_{g} \times _{g}\mu_{a} = \frac{1}{_{g}\mu_{a}} \times _{g}\mu_{a} = 1 \]

This product is always 1 regardless of whether the surfaces are parallel or not.


Step 4: Final Answer:

The product of the ratios is 1.
Quick Tip: The product of refractive indices for a series of media starting and ending in the same medium is always unity (\( \mu_{12} \times \mu_{23} \times \mu_{31} = 1 \)).

Step 1: Understanding the Concept:

In a rectangular glass block with parallel opposite faces, the normals at the point of incidence on both faces are parallel to each other.


Step 2: Detailed Explanation:

If the surfaces were parallel, the ray inside the glass would act as a transversal between two parallel normals.

This would mean the angle of refraction at the first surface (\( r_{1} \)) and the angle of incidence at the second surface (\( i_{2} \)) would be alternate interior angles, making them equal (\( r_{1} = i_{2} \)).

The question states that \( r_{1} \) is not the same as \( i_{2} \).

Therefore, the normals are not parallel, which implies the surfaces are not parallel.


Step 3: Final Answer:

The opposite surfaces are not parallel.
Quick Tip: If the surfaces of a glass block are not parallel, the emergent ray will not be parallel to the incident ray, and a deviation is produced (like in a prism).

Step 1: Understanding the Concept:

Geometrical properties of parallel lines and transversals are applied to the path of light through a medium.


Step 2: Detailed Explanation:

For parallel surfaces, the normal at the first surface is parallel to the normal at the second surface.

The refracted ray inside the medium acts as a transversal.

In such a case, the angle of refraction at the first surface (\( r \)) and the angle of incidence at the second surface (\( i' \)) must be equal as they are alternate interior angles.

Since the question provides that these two angles are not equal (\( r \neq i' \)), the condition for parallel surfaces is violated.


Step 3: Final Answer:

The conclusion is reached based on the fact that \( r \neq i' \), which only happens when the refracting surfaces are inclined at an angle to each other.
Quick Tip: For a parallel-sided slab, the lateral displacement occurs, but the emergent ray remains parallel to the incident ray because \( \angle i_{1} = \angle e \).

Step 1: Understanding the Concept:

The refractive index (\( \mu \)) of a medium is defined as the ratio of the speed of light in vacuum (or air) to the speed of light in that medium.


Step 2: Key Formula or Approach:
\[ \mu = \frac{c}{v} \implies v = \frac{c}{\mu} \]


Step 3: Detailed Explanation:

Given:

Refractive index of glass (\( \mu \)) = 1.8

Speed of light in air (\( c \)) = \( 3 \times 10^{8} ms^{-1} \)

Calculation:
\[ v = \frac{3 \times 10^{8}}{1.8} \]
\[ v = \frac{30}{18} \times 10^{8} \]
\[ v = \frac{5}{3} \times 10^{8} \]
\[ v \approx 1.666... \times 10^{8} ms^{-1} \]

Rounding to two decimal places: \( v = 1.67 \times 10^{8} ms^{-1} \).


Step 4: Final Answer:

The speed of light in the glass is \( 1.67 \times 10^{8} ms^{-1} \).
Quick Tip: Speed of light decreases in a denser medium. Since \( \mu > 1 \), the speed \( v \) will always be less than \( 3 \times 10^{8} ms^{-1} \).

Step 1: Understanding the Concept:

The speed of light in a medium is a characteristic property of the material of the medium and the wavelength of light used.


Step 2: Detailed Explanation:

The speed of light in a medium depends on its refractive index (\( v = c/\mu \)).

The refractive index depends on the nature of the material (optical density) and the frequency/wavelength of the light.

Changing the physical dimensions (width, height, or thickness) of the block does not change the material or the optical density.

Therefore, the refractive index remains 1.8, and the speed of light remains unchanged.


Step 3: Final Answer:

The speed of light in the block remains \( 1.67 \times 10^{8} ms^{-1} \).
Quick Tip: Intrinsic properties like refractive index, density, and specific heat capacity do not depend on the size or shape of the object.

Step 1: Understanding the Concept:

Specific electromagnetic radiations can cause certain substances to fluoresce (glow), which is used for security identification.


Step 2: Detailed Explanation:

Genuine currency notes have certain marks or patterns printed with special fluorescent ink.

These marks are invisible under ordinary visible light but become visible and glow when exposed to Ultraviolet (UV) radiations.

Fake currency usually lacks these sophisticated fluorescent security features.


Step 3: Final Answer:

Ultraviolet radiations are used to detect fake currency.
Quick Tip: UV radiations have high energy and short wavelengths, making them ideal for exciting electrons in fluorescent materials.

Step 1: Understanding the Concept:

When light travels from a denser to a rarer medium, it undergoes Total Internal Reflection (TIR) if the angle of incidence is greater than the critical angle.


Step 2: Detailed Explanation:

1. The ray AB enters the first surface of the right-angled prism normally (\( \angle i = 0^\circ \)). It travels undeviated and hits the hypotenuse.

2. Based on the prism geometry (angle \( 30^\circ \)), the angle of incidence at the hypotenuse is \( 60^\circ \).

3. The critical angle (\( C \)) is given as \( 42^\circ \).

4. Since \( 60^\circ > 42^\circ \), the ray undergoes Total Internal Reflection.

5. The reflected ray follows the law of reflection (\( \angle i = \angle r = 60^\circ \)) and moves toward the third surface.

6. Depending on the specific geometry of the emergence, it will refract out into the air.


Step 3: Final Answer:

The ray undergoes TIR at the hypotenuse because the angle of incidence (\( 60^\circ \)) exceeds the critical angle (\( 42^\circ \)).
Quick Tip: In a right-angled prism, always check the angle of incidence at the internal face. If \( i > C \), reflect the ray; if \( i < C \), refract it out.

Step 1: Understanding the Concept:

A convex lens forms a real, inverted image of the same size when the object is at \( 2f \). Magnification \( m = v/u \).


Step 2: Key Formula or Approach:

Magnification for lens: \( m = \frac{f}{f+u} \) (Using sign convention)


Step 3: Detailed Explanation:

Case 1: Image same size as object.

This happens when object distance \( u_{1} = -2f \). Magnification \( m_{1} = -1 \).

Case 2: Object is moved 12 cm closer.

New object distance \( u_{2} = -(2f - 12) = -2f + 12 \).

New magnification \( m_{2} = -3 \) (Real image is inverted).

Using the formula \( m = \frac{f}{f+u} \):
\[ -3 = \frac{f}{f + (-2f + 12)} \]
\[ -3 = \frac{f}{12 - f} \]
\[ -3(12 - f) = f \]
\[ -36 + 3f = f \]
\[ 2f = 36 \implies f = 18 cm \]


Step 4: Final Answer:

The focal length of the convex lens is 18 cm.
Quick Tip: For convex lenses: \( m = 1 \implies u = 2f \). This is a standard result that serves as a starting point for many problems.

Step 1: Understanding the Concept:

Phase change (melting) requires the absorption of latent heat from the surroundings.


Step 2: Detailed Explanation:

After a hailstorm, the hail (ice) on the ground begins to melt.

To melt, ice requires latent heat of fusion (\( 336 J/g \)). It absorbs this massive amount of heat from the surrounding air.

As the atmosphere loses heat to the melting ice, its temperature drops significantly.

Therefore, the atmosphere feels much colder after the hailstorm than during it.


Step 3: Final Answer:

The statement is False.
Quick Tip: Melting of ice is an endothermic process; it "steals" heat from the environment, causing a cooling effect.

Step 1: Understanding the Concept:

Specific Heat Capacity is independent of mass, but Heat Capacity depends directly on mass.


Step 2: Detailed Explanation:

The thermal energy required to raise the temperature of a body by \( 1^\circC \) is called its Heat Capacity (\( C' \)).

It is calculated as: \( C' = m \times c \), where \( m \) is mass and \( c \) is specific heat capacity.

By making the base of the frying pan heavier, we are increasing its mass (\( m \)).

Since the material is the same, \( c \) is constant, but the product \( m \times c \) increases.

Therefore, the heat capacity of the pan increases.


Step 3: Final Answer:

The Heat Capacity (Thermal Capacity) of the pan changes (increases).
Quick Tip: Cooking utensils are often made with thick bases to increase heat capacity, which helps in maintaining a steady temperature and preventing food from burning.

Step 1: Understanding the Concept:

This principle is based on the Law of Conservation of Energy.


Step 2: Detailed Explanation:

The principle of Calorimetry states that when two bodies of different temperatures are placed in thermal contact, heat flows from the hot body to the cold body until thermal equilibrium is reached.

If no heat is lost to the surroundings, then:
\[ Heat energy lost by the hot body = Heat energy gained by the cold body \]

This assumes the system is perfectly insulated.


Step 3: Final Answer:

The principle states that heat lost equals heat gained in an isolated system.
Quick Tip: In numericals, always set \( m_{1}c_{1}(T_{1}-T) = m_{2}c_{2}(T-T_{2}) \), where \( T \) is the final mixture temperature.

Step 1: Understanding the Concept:

During a phase change (like freezing), the temperature of a substance remains constant even though it is losing heat.


Step 2: Detailed Explanation:

On a cooling curve (temperature vs. time graph), a phase change is represented by a horizontal plateau (a line with zero slope).

In the provided graph, the segment QR is horizontal.

The temperature corresponding to this horizontal part is \( 20^\circC \).

This indicates that the liquid is freezing into a solid at this constant temperature.


Step 3: Final Answer:

The freezing temperature is \( 20^\circC \).
Quick Tip: For a pure substance, the freezing point and the melting point are the same temperature.

Step 1: Understanding the Concept:

Cooling involves the removal of heat, leading to a transition from a higher energy state (liquid) to a lower energy state (solid).


Step 2: Detailed Explanation:

The curve starts from a higher temperature (liquid phase PQ).

The region QR is the transition period where temperature is constant while heat is being released (Latent heat of fusion).

Since the substance is being cooled and the temperature is constant, it is changing from the liquid state to the solid state.

This process is known as freezing or solidification.


Step 3: Final Answer:

The phase change is freezing.
Quick Tip: Horizontal lines in thermal graphs always signify latent heat being exchanged during a change of state.

Step 1: Understanding the Concept:

The rate of cooling (rate of temperature drop) is indicated by the slope of the cooling curve.


Step 2: Detailed Explanation:

The slope of the curve represents how fast the temperature is changing over time (\( \Delta T / \Delta t \)).

- Region PQ (Liquid): Temperature drops from \( 45^\circC \) to \( 20^\circC \) in 20 seconds. Slope = \( 25/20 = 1.25^\circC/s \).

- Region RS (Solid): Temperature drops from \( 20^\circC \) to \( 0^\circC \) in 5 seconds (from 30s to 35s). Slope = \( 20/5 = 4^\circC/s \).

Since the slope is much steeper in the RS region, the temperature falls much faster in the solid state.

Assuming heat is lost to the same environment, a faster temperature drop implies heat is being liberated at a faster rate or the specific heat is lower.


Step 3: Final Answer:

The substance liberates heat at a faster rate in the solid state because the slope of the curve is steeper in region RS compared to PQ.
Quick Tip: Steeper Slope = Faster Cooling = Faster Heat Liberation. Always compare the "rise over run" of the different diagonal segments.

Step 1: Understanding the Concept:

For a convex lens, a real image of the same size as the object is formed on a screen when the object is placed at a distance of twice the focal length (\( 2f \)) from the lens.

Magnification (\( m \)) is given by the ratio of image distance (\( v \)) to object distance (\( u \)).


Step 2: Key Formula or Approach:

1. Lens formula: \( \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \)

2. Magnification formula: \( m = \frac{v}{u} = \frac{f}{f + u} \)


Step 3: Detailed Explanation:

Case 1: Image of same size (\( m = -1 \)) on a screen (real image).

This implies \( u_1 = -2f \).

Case 2: Object is moved 12 cm closer to the lens.

New object distance, \( u_2 = u_1 + 12 = -2f + 12 \).

The new image is real and three times the size, so \( m = -3 \).

Using the magnification formula \( m = \frac{f}{f + u} \):
\[ -3 = \frac{f}{f + (-2f + 12)} \]
\[ -3 = \frac{f}{12 - f} \]

Multiplying both sides by \( (12 - f) \):
\[ -3(12 - f) = f \]
\[ -36 + 3f = f \]
\[ 2f = 36 \implies f = 18 cm \]


Step 4: Final Answer:

The focal length of the lens is 18 cm.
Quick Tip: Remember that for a real image formed by a lens, magnification is negative. If \( m = -1 \), the object is at \( 2f \). Use the \( m = \frac{f}{f+u} \) formula to save time in lens problems.

Step 1: Understanding the Concept:

This question involves the concept of Latent Heat of Fusion. Melting is an endothermic process.


Step 2: Detailed Explanation:

After a hailstorm, the hail (ice) present on the ground begins to melt.

To change its state from solid to liquid, ice absorbs a large amount of heat (specific latent heat of fusion \( = 336 J/g \)) from the surrounding atmosphere.

Because the surrounding air loses this heat to the melting ice, its temperature drops significantly.

Therefore, the atmosphere becomes much colder after a hailstorm than during it.


Step 3: Final Answer:

The statement is False.
Quick Tip: Melting of ice always causes cooling of the surroundings because it "steals" energy to break molecular bonds. This is why it feels colder when it starts to thaw after a heavy snowfall.

Step 1: Understanding the Concept:

We must distinguish between specific heat capacity and heat capacity. Specific heat is intrinsic to the material, while heat capacity depends on the mass.


Step 2: Key Formula or Approach:

Heat Capacity (\( C' \)) \( = m \times c \), where \( m \) is mass and \( c \) is specific heat capacity.


Step 3: Detailed Explanation:

By making the base of the frying pan heavier, we are increasing its mass (\( m \)).

The material of the pan remains the same, so the specific heat capacity (\( c \)) remains constant.

However, since the mass increases, the product \( m \times c \) increases.

This product is the heat capacity (or thermal capacity) of the pan.


Step 4: Final Answer:

The physical quantity that changes is the Heat Capacity (Thermal Capacity).
Quick Tip: Heavy-bottomed pans are preferred in cooking because their higher heat capacity allows them to store more thermal energy and distribute it more evenly, preventing food from burning quickly.

Step 1: Understanding the Concept:

Calorimetry is based on the law of conservation of energy applied to thermal systems.


Step 2: Detailed Explanation:

The principle of calorimetry states that when two bodies of different temperatures are placed in thermal contact, heat flows from the hot body to the cold body until thermal equilibrium is reached.

In an isolated system (where no heat is lost to the surroundings):

Heat lost by the hot body \( = \) Heat gained by the cold body.

Mathematically: \( m_1 c_1 \Delta T_1 = m_2 c_2 \Delta T_2 \).


Step 3: Final Answer:

The principle states that in an insulated system, the total heat lost by a hot body is equal to the total heat gained by a cold body.
Quick Tip: This principle assumes a "perfectly insulated" environment. In practical exams, always mention that "no heat is lost to the surroundings" for a complete definition.

Step 1: Understanding the Concept:

On a cooling curve (temperature vs. time), a phase change (like freezing) is represented by a horizontal plateau where the temperature remains constant.


Step 2: Detailed Explanation:

Looking at the provided graph:

1. The temperature falls from \( 50^\circC \) to \( 20^\circC \) (Region PQ).

2. From time \( t = 20 s \) to \( t = 30 s \) (Region QR), the temperature remains constant at \( 20^\circC \).

3. This constant temperature period indicates the change of state from liquid to solid.


Step 3: Final Answer:

The freezing temperature of the liquid is \( 20^\circC \).
Quick Tip: Horizontal lines in thermal graphs always indicate a phase change (melting, freezing, or boiling) because the temperature does not change while the state is shifting.

Step 1: Understanding the Concept:

A cooling curve follows a substance as it loses heat. Transitioning from a liquid to a solid at a constant temperature is freezing.


Step 2: Detailed Explanation:

In the region PQ, the substance is a liquid being cooled.

In the region QR, the temperature is constant while the substance continues to lose heat to the surroundings.

This represents the latent heat of fusion being released as the liquid turns into a solid.

This process is called freezing or solidification.


Step 3: Final Answer:

The phase change occurring in region QR is freezing.
Quick Tip: If the graph were going "up" (heating), this region would represent melting. Since it is a cooling curve (going "down"), it is freezing.

Step 1: Understanding the Concept:

The rate of cooling (rate of temperature fall) is represented by the slope of the temperature-time graph. A steeper slope indicates a faster rate of cooling.


Step 2: Detailed Explanation:

1. Liquid State (PQ): Temperature falls from \( 50^\circC \) to \( 20^\circC \) in \( 20 s \).

Rate of fall \( = \frac{50 - 20}{20} = \frac{30}{20} = 1.5^\circC/s \).

2. Solid State (RS): Temperature falls from \( 20^\circC \) to \( 0^\circC \) in \( 5 s \) (from \( 30 s \) to \( 35 s \)).

Rate of fall \( = \frac{20 - 0}{5} = 4^\circC/s \).

Since the slope is much steeper in the RS region than in the PQ region, the substance loses temperature more quickly in the solid state. This implies it liberates heat to the surroundings at a faster rate during this interval.


Step 3: Final Answer:

The substance liberates heat at a faster rate in the solid state because the slope of the cooling curve in region RS is steeper than in region PQ.
Quick Tip: Slope of cooling curve \( = \frac{\Delta T}{\Delta t} \). Larger slope \( \implies \) faster cooling. This often happens because the specific heat capacity of the solid phase is lower than that of the liquid phase.

Step 1: Understanding the Concept:

The moment of force (torque) is the turning effect of a force about a pivot.

By convention, clockwise moments are taken as negative, and anti-clockwise moments are taken as positive.


Step 2: Detailed Explanation:

1. Pivot is at point O.

2. Force \(F_{1}\) acts such that it tends to rotate the wheel in the clockwise direction.

3. Force \(F_{2}\) also acts such that it tends to rotate the wheel in the clockwise direction.

Since both forces tend to produce a clockwise rotation, both produce a negative moment.


Step 3: Final Answer:

Both forces \(F_{1}\) and \(F_{2}\) produce a negative moment because they both cause clockwise rotation about the pivot O.
Quick Tip: Always use the Right-Hand Rule or simply visualize the rotation: Clockwise = Negative (\(-\)), Anti-clockwise = Positive (\(+\)).

Step 1: Understanding the Concept:

For a body to be in rotational equilibrium, the algebraic sum of the moments of all forces acting on it about the pivot must be zero.


Step 2: Detailed Explanation:

As identified in part (a), both forces \(F_{1}\) and \(F_{2}\) produce clockwise moments.

Net Moment = Moment due to \(F_{1}\) + Moment due to \(F_{2}\).

Since both moments have the same sign (negative), their sum cannot be zero.

Because there is a non-zero net moment acting on the wheel, it is not in rotational equilibrium.


Step 3: Final Answer:

No, the wheel is not in equilibrium.
Quick Tip: Equilibrium requires the net force and the net torque to be zero. Here, the net torque is clearly non-zero.

Step 1: Detailed Explanation:

A body is in equilibrium only when the sum of anti-clockwise moments equals the sum of clockwise moments.

In this specific case, both forces \(F_{1}\) and \(F_{2}\) are producing moments in the clockwise direction.

Let \(\tau_{1}\) and \(\tau_{2}\) be the magnitudes of the moments. The total moment is \(- (\tau_{1} + \tau_{2})\).

Since \(\tau_{1} + \tau_{2} \neq 0\), the wheel will experience a net clockwise torque and will rotate.


Step 2: Final Answer:

The wheel is not in equilibrium because the total moment acting on the wheel about point O is non-zero (specifically, it is a net clockwise moment).
Quick Tip: In exams, always mention the "Principle of Moments" when justifying rotational equilibrium.

Step 1: Understanding the Concept:

In subatomic physics (dealing with atoms and particles), the Joule is often too large a unit to be practical.


Step 2: Detailed Explanation:

The electron volt (eV) is defined as the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt.

Relationship with SI unit:
\(1 eV = 1.602 \times 10^{-19} Joules \).


Step 3: Final Answer:

The unit of work/energy used in the subatomic scale is the electron volt (eV).
Quick Tip: Remember \(1 eV = 1.6 \times 10^{-19} J\). Larger units include keV, MeV, and GeV.

Step 1: Understanding the Concept:

Levers are classified based on the relative positions of the Fulcrum (F), Load (L), and Effort (E).


Step 2: Detailed Explanation:

In a pair of scissors:

1. The pivot point (screw) is the Fulcrum, which is located in the middle.

2. The effort is applied at the handles by the fingers.

3. The load (the object being cut) is at the blades.

Since the Fulcrum is between the Effort and the Load, it is a Class I lever.


Step 3: Final Answer:

Scissors belong to Class I levers.
Quick Tip: Mnemonic: FLE 123. (1=F in middle, 2=L in middle, 3=E in middle).

Step 1: Understanding the Concept:

Work done is defined as the product of the component of force in the direction of displacement and the magnitude of the displacement: \(W = F \cdot s \cdot \cos(\theta)\).


Step 2: Key Formula or Approach:
\(W = Force \times Displacement in the direction of force\).


Step 3: Detailed Explanation:

Let \(F\) be the constant force magnitude.

1. Case 2: Displacement is along the straight line AB. The force \(F\) is in the same direction as displacement.
\(s = 20 m\). \(W_{2} = F \times 20 = 20F\).

2. Case 3: Displacement is along AB (20 m), but the force acts at an angle \(\theta\).
\(W_{3} = F \cdot \cos(\theta) \times 20 = 20F \cos(\theta)\). Since \(0 < \theta < 90^{\circ}\), \(\cos(\theta) < 1\). Thus \(W_{3} < W_{2}\).

3. Case 1: The stone moves along the semi-circle arc AJB. The force \(F\) is shown acting along the tangent at every point (implied by the arrow following the curve).

Distance along arc = \(\pi \times radius = \pi \times \frac{20}{2} = 10\pi \approx 31.4 m\).
\(W_{1} = F \times 10\pi \approx 31.4F\).

Comparing values: \(20F \cos(\theta) < 20F < 31.4F\).


Step 4: Final Answer:

The ascending order is Case 3 \(<\) Case 2 \(<\) Case 1.
Quick Tip: Work depends on the distance moved along the line of the force. Curved paths generally involve more distance and thus potentially more work if force follows the path.

Step 1: Understanding the Concept:

Gravitational Potential Energy (P.E.) is the energy possessed by a body due to its position above the ground.


Step 2: Key Formula or Approach:
\(P.E. = mgh\)


Step 3: Detailed Explanation:

Given:

Mass, \(m = 20 g = \frac{20}{1000} kg = 0.02 kg\)

Height, \(h = 45 m\)

Acceleration due to gravity, \(g = 10 m/s^{2}\)
\[P.E. = 0.02 \times 10 \times 45\]
\[P.E. = 0.2 \times 45 = 9 J\]


Step 4: Final Answer:

The initial potential energy of the ball is 9 J.
Quick Tip: Always convert mass to SI units (kg) before substituting into physics formulas to get the answer in Joules.

Step 1: Understanding the Concept:

According to the law of conservation of energy, the potential energy at the top is converted into kinetic energy at the bottom (neglecting air resistance).


Step 2: Key Formula or Approach:
\(mgh = \frac{1}{2}mv^{2}\) or \(v = \sqrt{2gh}\)


Step 3: Detailed Explanation:

Initial Height, \(h = 45 m\)

Gravity, \(g = 10 m/s^{2}\)
\[v = \sqrt{2 \times 10 \times 45}\]
\[v = \sqrt{900}\]
\[v = 30 m/s\]


Step 4: Final Answer:

The speed of the ball when it hits the ground is 30 m/s.
Quick Tip: The speed of a falling body depends only on the height and gravity, not on the mass of the body.

Step 1: Understanding the Concept:

The loss in kinetic energy upon collision is the difference between the energy just before impact and the energy just after rebound.


Step 2: Key Formula or Approach:

Loss in Energy = Initial energy - Final energy after rebound.


Step 3: Detailed Explanation:

1. Total initial energy = 9 J (from part a).

2. Potential energy at rebound height (40 m):
\(P.E._{rebound} = mgh_{2} = 0.02 \times 10 \times 40 = 8 J\).

3. Since it reaches 40 m, its kinetic energy just after rebound must have been 8 J.

4. Loss in energy = \(9 J - 8 J = 1 J\).


Step 4: Final Answer:

The loss in kinetic energy on striking the ground is 1 J.
Quick Tip: Energy loss during collision is often converted into heat and sound energy.

Step 1: Understanding the Concept:

In an ideal situation, the Mechanical Advantage (M.A.) of a single fixed pulley is 1, and for a single movable pulley, it is 2.


Step 2: Key Formula or Approach:
\(M.A. = \frac{Load (L)}{Effort (E)}\)


Step 3: Detailed Explanation:

Given Load, \(L = 30 kgf\).

1. For Suhas (Fixed Pulley):
\(M.A. = 1 \implies E_{suhas} = L = 30 kgf\).

2. For Radha (Movable Pulley):
\(M.A. = 2 \implies E_{radha} = \frac{L}{2} = \frac{30}{2} = 15 kgf\).

Ratio = \(\frac{E_{suhas}}{E_{radha}} = \frac{30}{15} = \frac{2}{1}\).


Step 4: Final Answer:

The ratio of the efforts is 2 : 1.
Quick Tip: A single fixed pulley only changes the direction of effort, whereas a single movable pulley acts as a force multiplier.

Step 1: Understanding the Concept:

Potential Energy gained = \(mg \Delta h = L \times displacement of load\).


Step 2: Key Formula or Approach:

Velocity Ratio (\(V.R.\)) = \(\frac{Displacement of Effort (d_{E})}{Displacement of Load (d_{L})}\).


Step 3: Detailed Explanation:

Let the displacement of effort be \(d\) in both cases.

1. Suhas (Fixed Pulley): \(V.R. = 1 \implies d_{L} = d_{E} = d\).

Energy Gained (\(P.E._{1}\)) = \(L \times d\).

2. Radha (Movable Pulley): \(V.R. = 2 \implies d_{L} = \frac{d_{E}}{2} = \frac{d}{2}\).

Energy Gained (\(P.E._{2}\)) = \(L \times \frac{d}{2}\).

Ratio = \(\frac{P.E._{1}}{P.E._{2}} = \frac{L \times d}{L \times (d/2)} = \frac{2}{1}\).


Step 4: Final Answer:

The ratio of potential energy gained by the loads is 2 : 1.
Quick Tip: Even if efforts are moved same distance, the load in a movable pulley only rises half as high.

Step 1: Understanding the Concept:

Efficiency (\(\eta\)) is defined as the ratio of Work Output to Work Input.


Step 2: Detailed Explanation:

The question specifies "in an ideal situation". In an ideal situation, there is no friction, and the string/pulley are weightless.

For any ideal machine, the efficiency is always 100% or 1.
\(\eta_{suhas} = 100%\)
\(\eta_{radha} = 100%\)

Ratio = \(1 : 1\).


Step 3: Final Answer:

The ratio of the efficiencies is 1 : 1.
Quick Tip: "Ideal situation" is a keywords in physics problems indicating 100% efficiency.

Step 1: Understanding the Concept:

When a body is displaced from its mean position and released, it starts vibrating.


Step 2: Detailed Explanation:

The ruler vibrates with its own natural frequency. However, because it is vibrating in air, it faces air resistance, and energy is lost in every cycle. This causes the amplitude to decrease over time.

Technically, these are damped vibrations. If we ignore air resistance for a short duration, they can be called natural or free vibrations.


Step 3: Final Answer:
The vibrations produced are damped vibrations (or natural vibrations if damping is ignored).
Quick Tip: In real-world conditions, all "free" vibrations eventually die out because of damping.

Step 1: Understanding the Concept:

For a vibrating string or strip, the frequency is inversely proportional to the length of the vibrating part.


Step 2: Detailed Explanation:

When the ruler is pushed further onto the table, the length of the part projecting out (the vibrating length \(l\)) decreases.

Frequency \(f \propto \frac{1}{l}\).

Since the vibrating length is reduced, the frequency of vibration increases. This results in a shriller sound.


Step 3: Final Answer:

The frequency of vibration increases because the vibrating length of the ruler has decreased.
Quick Tip: Smaller length = Higher frequency = Higher pitch.

Step 1: Understanding the Concept:

An echo is heard when sound travels to a reflecting surface and back to the listener.


Step 2: Key Formula or Approach:
\(v = \frac{2d}{t} \implies d = \frac{v \times t}{2}\)


Step 3: Detailed Explanation:

Speed of sound, \(v = 340 m/s\)

Time for echo, \(t = 3 s\)

Let \(d\) be the distance of B from the cliff.
\[d = \frac{340 \times 3}{2}\]
\[d = 170 \times 3 = 510 m\]


Step 4: Final Answer:

The distance of person B from the cliff is 510 m.
Quick Tip: For echo problems, distance is always doubled (\(2d\)) because the sound must go to the wall and come back.

Step 1: Understanding the Concept:

The time taken for sound to travel directly from source to listener is simply Distance / Speed.


Step 2: Detailed Explanation:
Distance between A and B = 170 m.

Speed of sound = 340 m/s.

Time = \(\frac{Distance}{Speed}\)

Time = \(\frac{170}{340} = 0.5 s\).


Step 3: Final Answer:

Person B hears the gunshot from A after 0.5 s.
Quick Tip: This is direct sound travel, so do not double the distance!

Step 1: Understanding the Concept:

Loudness is a characteristic of sound that depends on the amplitude of the vibration.


Step 2: Detailed Explanation:

When a sound wave travels through air and reflects off a cliff, some of its energy is absorbed by the air and the surface of the cliff.

A decrease in energy results in a decrease in the amplitude of the wave.

Since loudness \(\propto Amplitude^{2}\), the sound becomes softer. The frequency (pitch) remains the same as it depends on the source.


Step 3: Final Answer:

The echo is softer due to the decrease in the amplitude of the wave.
Quick Tip: Frequency only changes with the source or relative motion (Doppler Effect). Loudness always changes with distance and absorption due to amplitude decay.

Step 1: Understanding the Concept:

In a parallel combination, the potential difference (voltage) across each component is the same.


Step 2: Detailed Explanation:

The diagram shows Bulb A and Bulb B connected in parallel across a 40 V source.

Voltmeters \(V_{1}\) and \(V_{2}\) are connected across Bulb A and Bulb B respectively.

Since they are in parallel:

Voltage across A = Voltage across B = Supply voltage = 40 V.

Therefore, \(V_{1} = 40 V\) and \(V_{2} = 40 V\).

Ratio = \(40 : 40 = 1 : 1\).


Step 3: Final Answer:

The ratio \(V_{1} : V_{2}\) is 1 : 1.
Quick Tip: In parallel circuits, Voltage is constant. In series circuits, Current is constant.

Step 1: Understanding the Concept:

Total current in a parallel circuit is the sum of currents in individual branches.


Step 2: Detailed Explanation:

Total Current \(I_{total} = I_{A} + I_{B}\).

If Bulb A fuses, the branch with Bulb A becomes an open circuit, and current \(I_{A}\) becomes zero.

The total current drawn from the source will now only be \(I_{B}\).

Therefore, the total main current decreases. It does not remain the same.


Step 3: Final Answer:

False. The total current in the main circuit decreases when one parallel branch fails.
Quick Tip: In home wiring (parallel), turning off one light reduces the total bill (current) because total resistance increases.

Step 1: Understanding the Concept:

Standard color coding and positioning for a three-pin plug (viewed from the back):

- Top pin: Earth (Green/Yellow)

- Right pin: Neutral (Blue/Black)

- Left pin: Live (Red/Brown)

\textit{Note: When viewed from the front, L is right and N is left. From the back, it is mirrored.


Step 2: Detailed Explanation:

In the diagram provided:

1. The Earth pin (top) is connected correctly (green).

2. However, looking at the two lower pins from the reverse side, the Red wire (Live) should be on the left and the Blue wire (Neutral) should be on the right.

The diagram shows the Red wire on the right and the Blue wire on the left. They are incorrectly swapped.


Step 3: Final Answer:

The fault is that the Live wire (Red) and Neutral wire (Blue) are connected to the wrong pins (swapped).
Quick Tip: Mnemonic for front view: L is for Live and Left? No! For front view: L is Right, N is Left. Back view: L is Left, N is Right.

Step 1: Understanding the Concept:

Safety devices like switches and fuses are always connected in the Live wire.


Step 2: Detailed Explanation:

If the wires are swapped, the switch of the appliance will now be in the Neutral line.

When the switch is turned 'OFF', the circuit is broken, but the appliance remains connected to the high voltage through the Live wire (which is now connected where the Neutral should be).

A user touching the internal parts of the "OFF" appliance could receive a fatal electric shock.


Step 3: Final Answer:

The main risk is that the appliance remains at a high potential even when switched off, leading to a risk of electric shock.
Quick Tip: Switches must always be in the Live wire so that turning them off makes the appliance "dead" (at 0V).

Step 1: Understanding the Concept:

Most AC appliances require a complete path for current to flow, regardless of the polarity (for simple resistive loads).


Step 2: Detailed Explanation:

The appliance requires a potential difference of 220V between its terminals to operate.

Even with the wires swapped, a complete path exists from the Live terminal through the appliance to the Neutral terminal.

The current will still flow, and the appliance will work, although it is highly unsafe.


Step 3: Final Answer:

Yes, the appliance will function, but it will be extremely dangerous to use.
Quick Tip: "Working" does not mean "Safe". Swapped wiring is a common cause of home accidents.

Step 1: Understanding the Concept:

When a switch is open, the branch containing it does not conduct current.


Step 2: Detailed Explanation:

If switch S is open, the circuit consists of two parallel branches:

Branch 1 (Top): \(12 \(\Omega\)\) and \(6 \text{ \(\Omega\)\) in series. \(R_{1 = 12 + 6 = 18 \(\Omega\)\).

Branch 2 (Bottom): \(6 \text{ \(\Omega\)\) and \(12 \text{ \(\Omega\)\) in series. \(R_{2 = 6 + 12 = 18 \(\Omega\)\).

Now, \(R_{1\) and \(R_{2}\) are in parallel:
\[\frac{1}{R_{AB}} = \frac{1}{18} + \frac{1}{18} = \frac{2}{18} = \frac{1}{9}\]
\(R_{AB} = 9 \text{ \(\Omega\)\).


Step 3: Final Answer:

The resistance across AB when S is open is 9 \(\Omega\).
Quick Tip: When two equal resistors \(R\) are in parallel, the equivalent resistance is \(R/2\). Here, \(18/2 = 9 \Omega\).

Step 1: Understanding the Concept:

When the switch S is closed, the junctions between the resistors are connected. This reconfigures the series/parallel relationships.


Step 2: Detailed Explanation:

With S closed, the circuit becomes:

1. A parallel pair of \(12 \(\Omega\)\) and \(6 \text{ \(\Omega\)\) on the left.

Left equivalent resistance \(R_{L = \frac{12 \times 6}{12 + 6} = \frac{72}{18} = 4 \(\Omega\)\).

2. A parallel pair of \(6 \text{ \(\Omega\)\) and \(12 \text{ \(\Omega\)\) on the right.

Right equivalent resistance \(R_{R = \frac{6 \times 12}{6 + 12} = \frac{72}{18} = 4 \(\Omega\)\).

3. These two equivalent resistors are now in series:
\(R_{AB = R_{L} + R_{R} = 4 + 4 = 8 \text{ \(\Omega\)\).


Step 3: Final Answer:

The resistance across AB when S is closed is 8 \(\Omega\).
Quick Tip: Closing a bridge switch usually decreases the total resistance of the network.

Step 1: Understanding the Concept:

The fuse is a safety device that prevents excessive current from flowing through an appliance.

The rating of a fuse is determined by the maximum current the appliance draws during normal operation.


Step 2: Key Formula or Approach:

Electrical Power (\( P \)) is the product of Voltage (\( V \)) and Current (\( I \)).
\[ I = \frac{P}{V} \]


Step 3: Detailed Explanation:

Given:

Power (\( P \)) = 1100 W

Voltage (\( V \)) = 220 V

Substituting the values into the formula:
\[ I = \frac{1100}{220} \]
\[ I = 5 A \]

The current drawn by the electric iron is 5 A. Therefore, a fuse with a minimum rating of 5 A is required to allow the appliance to function normally.


Step 4: Final Answer:

The minimum rating of the fuse required is 5 A.
Quick Tip: In practical scenarios, a fuse rating is chosen to be slightly higher than the operating current (e.g., a 6 A fuse for a 5 A load) to account for minor fluctuations without blowing unnecessarily.

Step 1: Understanding the Concept:

Electrical energy is the total power consumed over a specific period. The commercial unit for electrical energy is the kilowatt-hour (kWh).


Step 2: Key Formula or Approach:

Energy (\( E \)) in kWh = Power (\( P \)) in kW \(\times\) Time (\( t \)) in hours.


Step 3: Detailed Explanation:

First, convert the power from Watts to Kilowatts:
\[ P = \frac{1100}{1000} kW = 1.1 kW \]

Given time \( t = 5 hours \).

Calculate Energy:
\[ E = 1.1 kW \times 5 h \]
\[ E = 5.5 kWh \]


Step 4: Final Answer:

The energy consumed by the electric iron is 5.5 kWh.
Quick Tip: Always ensure units are consistent. If power is in Watts, divide by 1000 to get kW. If time is in minutes, divide by 60 to get hours.

Step 1: Understanding the Concept:

One "unit" of electricity as billed by utility companies is exactly 1 kWh. The total cost is the product of units consumed and the rate per unit.


Step 2: Detailed Explanation:

From the previous calculation, the energy consumed is 5.5 kWh.

Units consumed = 5.5 units.

Rate per unit = \₹ 10.
\[ Total Cost = Units \times Rate \]
\[ Total Cost = 5.5 \times 10 = 55 \]


Step 3: Final Answer:

The total cost of the energy consumed is ₹ 55.
Quick Tip: To find monthly costs, calculate energy per day and multiply by the number of days in the month.

Step 1: Understanding the Concept:

Faraday's Law of Electromagnetic Induction states that an EMF is induced in a coil only when there is a change in the magnetic flux linked with it. This change is caused by relative motion between the magnet and the coil.


Step 2: Detailed Explanation:

In the given scenario, the magnet moves to the left at \( 5 ms^{-1} \) and the coil also moves to the left at \( 5 ms^{-1} \).

Since both are moving with the same velocity in the same direction, the distance between them remains constant.

Relative velocity = \( 5 ms^{-1} - 5 ms^{-1} = 0 ms^{-1} \).

Because there is no relative motion, there is no change in the magnetic flux linked with the coil.

Consequently, no current is induced, and the galvanometer shows zero deflection.


Step 3: Final Answer:

The deflection becomes zero because the relative velocity between the magnet and the coil is zero.
Quick Tip: Induced current depends on \( \frac{d\phi}{dt} \). If relative position is constant, flux \( \phi \) is constant, and its derivative is zero.

Step 1: Understanding the Concept:

The magnitude of induced EMF is proportional to the rate of relative motion. The direction of induced current depends on whether the magnetic flux is increasing or decreasing.


Step 2: Detailed Explanation:

The magnet moves to the left at \( 5 ms^{-1} \).

The coil moves to the right at \( 5 ms^{-1} \).

Since they move toward each other, their relative speed is the sum of their individual speeds:

Relative Velocity = \( 5 ms^{-1} + 5 ms^{-1} = 10 ms^{-1} \).

1. Magnitude: The relative speed is now double the original speed (\( 10 ms^{-1} \) vs \( 5 ms^{-1} \)). Therefore, the rate of change of flux is doubled, leading to a doubling of the induced current and deflection magnitude.

2. Direction: The magnet's North pole is still approaching the coil (flux is increasing). According to Lenz's Law, the direction of the induced current will be the same as in the original case (to the right).


Step 3: Final Answer:

The deflection magnitude increases (doubles) and the direction remains to the right.
Quick Tip: Moving towards each other: Relative speed = \( v_1 + v_2 \). Moving in same direction: Relative speed = \( |v_1 - v_2| \).

Step 1: Understanding the Concept:

Nuclear radiation (like Gamma rays) can easily penetrate most materials and damage human tissue. Shielding is required using materials that can effectively absorb or scatter these high-energy photons.


Step 2: Detailed Explanation:

Lead is the standard material used for radiation shielding in medical and nuclear fields. Workers wear aprons lined with lead (lead aprons) to protect their internal organs from accidental exposure to ionizing radiation.


Step 3: Final Answer:

The element used is Lead.
Quick Tip: Lead is used not only in aprons but also in the walls of X-ray rooms and containers for radioactive isotopes.

Step 1: Understanding the Concept:

The absorption of high-energy radiation depends on the interaction of photons with electrons. Denser materials with more electrons per atom provide better protection.


Step 2: Detailed Explanation:

Lead is preferred because:

1. High Density: Lead is very dense (\( 11.3 g/cm^3 \)), meaning atoms are packed closely together, leaving very little space for radiation to pass through without collision.

2. High Atomic Number (Z = 82): A high atomic number means each atom has many electrons. High-energy radiation interacts more frequently with these electrons via the photoelectric effect and Compton scattering, thus getting absorbed effectively.


Step 3: Final Answer:

Lead is preferred due to its high density and high atomic number, which enable it to absorb harmful ionizing radiation effectively.
Quick Tip: Materials with high "Z" (Atomic Number) are the most efficient at stopping electromagnetic radiations like X-rays and Gamma rays.

Step 1: Understanding the Concept:

Radioactive decay involves the emission of Alpha, Beta, or Gamma radiation. These are distinguished by their charge and their effect on the nucleus.


Step 2: Detailed Explanation:

1. Alpha (\( \alpha \)): Reduces mass number by 4. Deflected by magnetic field.

2. Beta (\( \beta \)): Consists of electrons (\( \beta^- \)) or positrons (\( \beta^+ \)). It has negligible mass, so it does not alter the mass number. Because it is charged, it is deflected by a magnetic field.

3. Gamma (\( \gamma \)): No change in mass or atomic number. Not deflected by magnetic fields (neutral).

The description provided matches the properties of Beta radiation.


Step 3: Final Answer:

The type of nuclear radiation emitted is Beta radiation.
Quick Tip: Beta particles are deflected much more than alpha particles in the same magnetic field due to their significantly smaller mass.

Step 1: Understanding the Concept:

During Beta-minus decay, a neutron inside the nucleus transforms into a proton. This increases the atomic number by 1 while keeping the mass number constant.


Step 2: Detailed Explanation:

Parent Nucleus: \( ^{24}_{11}Na \)

Mass number (\( A \)) = 24 (stays the same)

Atomic number (\( Z \)) = 11 (increases by 1 \(\rightarrow\) 12)

The element with atomic number 12 is Magnesium (Mg).

The particle emitted is an electron (\( ^{0}_{-1}e \) or \( \beta^- \)).

The decay equation is:
\[ ^{24}_{11}Na \rightarrow ^{24}_{12}Mg + ^{0}_{-1}e \]


Step 3: Final Answer:

The radioactive decay equation is \( ^{24}_{11}Na \rightarrow ^{24}_{12}Mg + \beta^- \).
Quick Tip: In nuclear equations, ensure the sum of the bottom numbers (atomic numbers/charges) and top numbers (mass numbers) are equal on both sides of the arrow.