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] ___________.


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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.

Answer 2

Answer:

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

\⟶I=mv−m(−v/2)[SignConvention]

I=3mv/2

Now,

Force × Time = Change in Momentum

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

⟶Mg×60/n=3mv/2

⟶v=120Mg/3mn

v = 40Mg/mn

Option (A) is correct.