Question

Two identical balls \( P \) and \( Q \) are moving with the same velocity. If the velocity of \( Q \) is reduced to zero and that of \( P \) is reduced to half, the ratio of change in temperatures of \( P \) to \( Q \) is:

• A. 4:3
• B. 1:4
• C. 3:4
• D. 1:2

Hint:

The rate of temperature change due to velocity is proportional to the square of the velocity.

Answer 1

The Correct Option is C

The change in temperature is proportional to the square of the velocity. Therefore, the ratio of temperature changes is: \[ \frac{\Delta T_P}{\Delta T_Q} = \frac{ \left( \frac{v_P}{2} \right)^2 }{v_Q^2} = \frac{1}{4} \] Thus, the ratio of temperature change is 3:4.