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: Understanding the Concept:
Force equals the rate of change of momentum, \(F = \frac{\Delta p}{t}\).

Step 2: Momentum change of one ball:
The ball hits normally with velocity \(+v\) and comes back with \(-v\). \(\Delta p = mv - (-mv) = 2mv\).

Step 3: All 100 balls:
They strike together, so the total change is \(100\times2mv = 200mv\).
\[ F = \frac{200mv}{t} \]

Step 4: Other options:
\(100mv/t\) would mean the balls stop, not reflect. \(200mvt\) has the wrong dependence on time. \(mv/100t\) is far too small.

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