### Center Of Mass Momentum And Collision Question 6

#### Question 6 - 31 January - Shift 1

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

(1) $\frac{100 mv}{t}$

(2) $\frac{200 mv}{t}$

(3) $200 mvt$

(4) $\frac{mv}{100 t}$

## Show Answer

#### Answer: (2)

#### Solution:

#### Formula: Conservation of Momentum

$ P_i=Nmv \hat{i} \quad \overrightarrow{{}P}_f=-Nm v \hat{i} $

$N$ is Number of balls strikes with wall

$N=100$

$ \begin{aligned} \Delta \overrightarrow{{}P} & =\overrightarrow{{}P}_f-\overrightarrow{{}P}_i=-2 Nm v \hat{i} \\ & =-200 Nm \hat{i} \end{aligned} $

$\overrightarrow{{}F} _{\text{Total }}=\frac{\Delta \overrightarrow{{}P}}{\Delta t}=-\frac{200 mvt}{t}$

$|\overrightarrow{{}F}|=\frac{200 mv}{t}$