Question

Two spheres $A$ and $B$ with masses in the ratio $2:3$ and specific heat $2:3$ fall freely rest. If the rest in their temperatures on reaching the ground in the ratio $1:2$ the ratio of their heights of fall is:-

• A. $3:1$
• B. $1:3$
• C. $4:3$
• D. $3:4$

Answer 1

Answer: (B)

$1:3$

$\text{Given:-}$ Mass ratio of two sphere A and B = 2:3

Specific heat of two sphere A and B = 2:3

Temperature ratio = 1:2

$\text{Solution:-}$ Potential energy of sphere = Thermal energy of sphere

$m_{A}g{h}_A=m_A{S}_A(\Delta T{)}_A..............(1)$

$m_{B}g{h}_B=m_B{S}_B(\Delta T{)}_B..............(2)$

Now divide equation 1 by 2, we get

$\frac{h_A}{h_B}=\left(\frac{S_A}{S_A}\right)\times \frac{\Delta T_A}{\Delta T_B}$

$\frac{h_A}{h_B}=\frac{2}{3}\times \frac{1}{2}$

$\Rightarrow \frac{h_A}{h_B}=\frac{1}{3}$

$\text{Hence the correct option is B}$