100 balls each of mass moving with speed simultaneously strike a wall normally and are reflected back with the same speed, in time s. The total force exerted by the balls on the wall is [2023]

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Solution

Q.
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 force exerted by the balls on the wall is [2023]

1 $\frac{100 m v}{t}$

2 $\frac{200 m v}{t}$

3 $200 m v t$

4 $\frac{m v}{100 t}$

Ans.
(2)

${\vec{P}}_{i} = N m v \hat{i}, {\vec{P}}_{f} = - N m v \hat{i}$

N is the number of balls striking the wall

$N = 100$

$Δ \vec{P} = {\vec{P}}_{f} - {\vec{P}}_{i} = - 2 N m v \hat{i} = - 200 N m v \hat{i}$

${\vec{F}}_{total} = \frac{Δ \vec{P}}{Δ t} = - \frac{200 m v t}{t}$

$| \vec{F} |$ $= \frac{200 m v}{t}$

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