Question

A disc of mass 0.2 kg is kept floating in air without falling by vertically firing bullets each of mass 0.05 kg on the disc at the rate of 10 bullets per every second. If the bullets rebound with the same speed, then the speed of each bullet is (Acceleration due to gravity = 10 m/s$^2$)

• A. 2 m/s
• B. 10 m/s
• C. 20 m/s
• D. 1 m/s

Hint:

Force = rate of change of momentum. For floating, upward force = weight.

Answer 1

The Correct Option is A

Let $M$ be the mass of the disc (0.2 kg), $m$ be the mass of each bullet (0.05 kg), and $n$ be the number of bullets fired per second (10 bullets/s). Let $v$ be the speed of each bullet. Since the bullets rebound with the same speed, the change in momentum of each bullet is $2mv$. The force exerted by the bullets on the disc is equal to the rate of change of momentum: $F = n(2mv) = 2nmv$. For the disc to float, this force must balance the weight of the disc: $F = Mg$ $2nmv = Mg$ $v = \frac{Mg}{2nm} = \frac{(0.2)(10)}{2(10)(0.05)} = \frac{2}{1} = 2$ m/s.