Question 79: 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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