Question 82: Centre of Mass and Rotational Motion

Question

100 balls each of mass $\mathrm{m}$ moving with speed $v$ simultaneously strike a wall normally and reflected back with same speed, in time $\mathrm{t ~s}$. The total force exerted by the balls on the wall is

Accepted Answer

When the balls strike the wall, the change in momentum of each ball is given by:
$\Delta p = mv - (-mv) = 2mv$
Since there are 100 balls, the total change in momentum of all the balls is $\Delta P = 2m(100v) = 200mv.$ The time taken for all the balls to strike the wall is $\mathrm{t}$ seconds. Therefore, the average force exerted on the wall is given by:
$F = \frac{\Delta P}{\mathrm{t}} = \frac{2m(100v)}{\mathrm{t}} = \frac{200mv}{\mathrm{t}}$
Therefore, the total force exerted by the balls on the wall is $\boxed{F = \frac{200mv}{\mathrm{t}}}$

Answer

$\frac{200 m v}{t}$

Answer

$\frac{100 m v}{t}$

Answer

$\frac{m v}{100 t}$

Answer

$200 m v t$

Centre of Mass and Rotational Motion

100 balls each of mass \mathrm{m} moving with speed v simultaneously strike a wall normally and reflected back with same speed, in time \mathrm{t ~s}. The total force exerted by the balls on the wall is

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