Question

\(100\) 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 magnitude of force exerted by the balls on the wall is

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

Hint:

Each ball changes momentum by \(2mv\); force is total change in momentum over time.

Answer 1

The Correct Option is B

Step 1: Plan:
Work with the impulse on the wall.

Step 2: Steps:
By Newton's third law, the force on the wall is equal and opposite to the force on the balls. The impulse given to the balls is $2mv$ each, so $200mv$ in total. Impulse equals $F\times t$, so $F = \frac{200mv}{t}$.

Final Answer:
The total force on the wall is $\frac{200mv}{t}$, option (B). \[ \boxed{\frac{200mv}{t}} \]