Q120 / 150 · MHT CET 2026 (13 April Shift 2) · Physics
$100$ balls each of mass $m$ moving with speed $v$ simultaneously strike a wall normally and reflected back with same speed, in time $t$ s. The total magnitude of force exerted by the balls on the wall is
- A$100mv/t$
- Correct answerB$200mv/t$
- C$200mvt$
- D$mv/100t$
Solution
Initial momentum of one ball is $p_i = mv$.
Final momentum of one ball after reflection is $p_f = -mv$.
Change in momentum of one ball is $\Delta p = p_f - p_i = -mv - mv = -2mv$.
Magnitude of change in momentum for one ball is $2mv$.
Total change in momentum for $100$ balls is $100 \times 2mv = 200mv$.
The total magnitude of force exerted on the wall is the rate of change of momentum, given by $F = \dfrac{\Delta p_{\text{total}}}{t} = \dfrac{200mv}{t}$.
Final momentum of one ball after reflection is $p_f = -mv$.
Change in momentum of one ball is $\Delta p = p_f - p_i = -mv - mv = -2mv$.
Magnitude of change in momentum for one ball is $2mv$.
Total change in momentum for $100$ balls is $100 \times 2mv = 200mv$.
The total magnitude of force exerted on the wall is the rate of change of momentum, given by $F = \dfrac{\Delta p_{\text{total}}}{t} = \dfrac{200mv}{t}$.
Hence, the correct answer is option: 'B'.