Question

A plate of mass M is held in air by firing bullets each of mass m with same velocity in vertically upward direction. If n bullets are fired per minute and each bullet strikes the plate with speed v and rebounds with half of the speed with which it strikes the plate, then the speed with which bullets are striking the plate is [Take g as acceleration due to gravity] ___________.

(a) $\frac{40Mg}{mn}$
(b) $\frac{2Mg}{3mn}$
(c) $\frac{120Mg}{nm}$
(d) $\frac{Mg}{20nm}$

From: ANTHE 2020 Mock Test Paper. (Class IXth Physics.) ​

Answer 1

Given Information,

• Mass of the Plate = M
• Mass of the bullets = m
• Velocity of bullets = v
• Velocity of rebound = v/2

Further, 'n' bullets are fired in a minute, implies 60/n bullets are fired in a second.

Now,

Impulse = Final Momenta - Initial Momenta

$\longrightarrow$ I = mv - m(- v/2) [Sign Convention]

$\longrightarrow$ I = 3mv/2

Now,

Force × Time = Change in Momentum

Since, the plate is held in air by forcing bullets. Applied Force = Weight = Mg.

$\longrightarrow$ Mg × 60/n = 3mv/2

$\longrightarrow$ v = 120Mg/3mn

$\longrightarrow$ v = 40Mg/mn

Option (A) is correct.