Question

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

• A. $1:2$
• B. $1:8$
• C. $1:4$
• D. $2:1$

Answer 1

Answer: (B)

$1:8$

Due to the same material both spheres will have the same specific heat.

Thermal capacity = Mass x Specific heat

Thermal capacity of the first sphere: $C_1=m_{1}S=4/3\left[\pi \right(r_1{)}^3\rho S]$

Thermal capacity of the second sphere: $C_2=m_{2}S=4/3\left[\pi \right(r_2^3\rho S]$

Thermal capacities are in the ratio of :

$C_1/C_2=\left(r_1{)}^3/\right(r_2{)}^3$

$=(1/2{)}^3$

$=1/8$

So, the correct option is $1:8$.