`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

Options

A. `(100mv)/(t)`
B. `200mvt`
C. `(200mv)/(t)`
D. `(mv)/(100t)`

Answer

To solve the problem, we need to calculate the total force exerted by 100 balls on the wall when they strike it and are reflected back. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the momentum change for one ball
When a ball of mass \( m \) strikes the wall with speed \( v \), its momentum before striking the wall is:
\[ p_{\text{initial}} = mv \]
After striking the wall and reflecting back, its momentum becomes:
\[ p_{\text{final}} = -mv \]
The change in momentum (\( \Delta p \)) for one ball is:
\[ \Delta p = p_{\text{final}} - p_{\text{initial}} = -mv - mv = -2mv \]

### Step 2: Calculate the force exerted by one ball
The force exerted by the ball can be calculated using the formula:
\[ F = \frac{\Delta p}{\Delta t} \]
Substituting the change in momentum:
\[ F = \frac{-2mv}{t} \]
Since force is a vector quantity, we consider the magnitude, which gives us:
\[ F = \frac{2mv}{t} \]

### Step 3: Calculate the total force for 100 balls
Since there are 100 balls, the total force (\( F_{\text{total}} \)) exerted by all the balls on the wall is:
\[ F_{\text{total}} = 100 \times F = 100 \times \frac{2mv}{t} = \frac{200mv}{t} \]

### Final Answer
Thus, the total force exerted by the 100 balls on the wall is:
\[ F_{\text{total}} = \frac{200mv}{t} \]