Question

Two spheres made of same material have their radii in the ratio
5:6, they are heated to the same temperature and kept in the same
surroundings at a moderate temperature. If the bodies are cooled by
natural process of radiation, the ratio of their initial rates of fall of
temperature is​

Answer 1

Answer:

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Answer 2

Given:

The ratio of radii of the spheres is 5:6

To Find:

The ratio of initial rates of fall of temperature of the spheres.

Solution:

The ratio of fall of temperature depends on the area of the spheres. From Newton's Law of Cooling  we know that rate of fall of temperature is directly proportional to the area and to the temperature difference of the surrounding and the body.

∴Newton's Law of cooling,

$\frac{dQ}{dt}\propto A\Delta T$

or $\frac{dQ}{dt}\propto A$

or $\frac{dQ}{dt}\propto r^2$

Now the ratio between rates of fall of temperature is

$\frac{(\frac{dQ}{dt})_1}{(\frac{dQ}{dt})_2} = (\frac{5}{6} )^2 = \frac{25}{36}$      (∵We have given ratio of radius of two spheres)

∴Required ratio is 25:36 .