Assertion (A): High thermal conductivity of metals is due to presence of free electrons.
Reason (R): Electrons at same temperature have very high average velocity than atoms.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true, free electrons are primary carriers of heat in metals. Reason (R) is true;
Electrons have higher velocity due to smaller mass at same kinetic energy. This high velocity enables efficient heat transfer, explaining (A). Both are true and (R) explains (A).
A solid sphere of copper of radius ( R ) and a hollow sphere of the same material of inner radius ( r ) and outer radius ( R ) are heated to the same temperature and allowed to cool in the same environment.
Assertion (A): Hollow sphere cools faster than solid sphere.
Reason (R): \( \left( \frac{d\theta}{dt} \right) \propto \frac{1}{m} \).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true. Hollow sphere has less mass ( m ) but same surface area ( A ) as solid sphere. Reason (R) is true, cooling rate \( \frac{dT}{dt} \propto \frac{A}{m} \). Since ( A ) is constant, \( \frac{dT}{dt} \propto \frac{1}{m} \). Lower mass ( m ) means faster cooling. Thus, both are true and (R) explains (A).
Assertion (A): A sphere, a cube and a thin circular plate made of same material and of same mass are initially heated to \( 200^{\circ}\text{C} \), the plate will cool at fastest rate.
Reason (R): Rate of cooling \( = \frac{\rho A \sigma}{ms} (T^4 – T_0^4) ) ( \propto \) surface area. Surface area is maximum for circular plate.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true because a thin plate has a larger surface area-to-mass ratio. Reason (R) states cooling rate \( \propto \) surface area, which is true \( \frac{dT}{dt} \propto \frac{A}{m}) \), and that a plate has the maximum surface area (for a given mass). Thus, both are true and (R) correctly explains (A).
Assertion (A): A body is emitting primarily red light. As the temperature of body is increased it may emit primarily yellow light.
Reason (R): Rate of radiation emitted by a body increases as the temperature increases.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true based on Wien's Displacement Law \( (\lambda_{\text{max}} T = b) \), where increasing ( T ) shifts \( \lambda_{\text{max}} \) to shorter wavelengths (red to yellow). Reason (R) is true based on Stefan-Boltzmann law \( (P \propto T^4) \). However, (R) explains the total radiated power, not the peak wavelength shift, so it's not the correct explanation for (A). Both are true, but (R) does not explain (A).
Assertion (A): A hot iron bar placed under a running tap loses heat by convection.
Reason (R): Convection involves flow of matter within a fluid due to unequal temperature of its parts.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true; heat loss from a hot bar to running water is a classic example of forced convection. Reason (R) correctly defines convection as heat transfer by bulk fluid movement due to temperature differences. Thus, both are true and (R) correctly explains (A).
Assertion (A): A temperature change which increases the length of a steel rod by ( 1% ) will increase its volume by ( 3% ).
Reason (R): The coefficient of volume expansion is nearly three times the coefficient of linear expansion.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true. If \( \frac{\Delta L}{L_0} = \alpha \Delta T = 0.01 \), then \( \frac{\Delta V}{V_0} = \gamma \Delta T \). Reason (R) is true, stating \( \gamma \approx 3\alpha \). Substituting, \( \frac{\Delta V}{V_0} \approx 3 (\alpha \Delta T) = 3(0.01) = 0.03 \), or ( 3% ). Thus, both are true and (R) correctly explains (A).
Assertion (A): Specific heat of substance is property of material.
Reason (R): Specific heat also depends on the condition of the experiment. The way in which heat is supplied to the body.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Specific heat is an intrinsic property of a substance, dependent only on the material itself and its phase, not on experimental conditions or how heat is supplied. Thus, Assertion (A) is true. Reason (R) is false. Therefore, (A) is true but (R) is false.
Assertion (A): When hot water is suddenly poured in cold beaker of thick glass, the beaker cracks.
Reason (R): Glass is bad conductor of heat and outer surface of the beaker does not expand.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Thick glass is a poor thermal conductor. When hot water is poured, the inner surface expands rapidly due to heating, while the outer surface remains cold and resists expansion.
This differential thermal expansion creates significant stress, causing the glass to crack. Both A and R are true, and R is the correct explanation for A.
Assertion (A): Ice is placed at top of the bucket to cold the water.
Reason (R): Heat transfer by convection takes place in upward direction.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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When ice is placed at the top, the water layer near the ice cools, becomes denser, and sinks. Warmer, less dense water from below rises to the top to be cooled by the ice. This sets up convection currents, efficiently cooling the entire volume. Thus, heat is transferred upwards to the ice by the rising warmer water. Both A and R are true, and R correctly explains A.
Assertion (A): Snow is better insulator than ice.
Reason (R): Snow contain air packet and air is bad conductor of heat.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Snow traps air, and air is a very poor conductor of heat. Therefore, snow acts as a better insulator than solid ice. Both assertion and reason are true, and the reason correctly explains the assertion.