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(B) Thermal capacity is defined as the product of mass $(m)$ and specific heat capacity $(c)$.Thermal Capacity $= m 	imes c = (V 	imes ho) 	imes

Vedclass · Accepted Answer

$1:8$

Vedclass · Answer

(B) Thermal capacity is defined as the product of mass $(m)$ and specific heat capacity $(c)$.Thermal Capacity $= m 	imes c = (V 	imes ho) 	imes c$,where $V$ is volume,$ho$ is density,and $c$ is specific heat.Since both spheres are made of the same substance,their density $(ho)$ and specific heat $(c)$ are identical.Therefore,the ratio of thermal capacities is equal to the ratio of their volumes.Volume of a sphere is given by $V = \frac{4}{3}\pi r^3$.Given the ratio of diameters is $1:2$,the ratio of radii $(r_1:r_2)$ is also $1:2$.Ratio of thermal capacities $= \frac{V_1}{V_2} = \frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3} = \left(\frac{r_1}{r_2}ight)^3 = \left(\frac{1}{2}ight)^3 = \frac{1}{8}$.Thus,the ratio is $1:8$.

Two spheres made of the same substance have diameters in the ratio $1:2$. Their thermal capacities are in the ratio of:

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