NEET Physics Question - Thermal Physics - Heat Transfer

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): \( \left( \frac{d\theta}{dt} \right) \propto \frac{1}{m} \).

Both (A) & (R) are true and the (R) is the correct explanation of the (A)

Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(A) is true but (R) is false

Both (A) and (R) are false

Solution:

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).

Rankers Physics

Cooling Rate of Solid vs. Hollow Sphere

Solution:

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