Question

A dish of mass $100gm$ is kept horizontally in air by firing bullets of mass $5g$ each at the rate of $10$ per second. If the bullets rebound with the same speed, what is the velocity with which the bullets are fired?

• A. $49cm/sec$
• B. $147cm/sec$
• C. $98cm/sec$
• D. $196cm/sec$

Answer 1

The correct option is C $98cm/sec$

Given: mass of disc $M=100g=0.1kg$ ,

mass of a bullet $m=5g=0.05kg$ ,

rate of strike $=10bullets/s$

The dish will be kept horizontally when its weight (downward force ) is balanced by the upward force, exerted by bullets on it .

Downward force, $F_D=Mg=0.1\times 9.8=0.98N$.

Now, let upward velocity of bullet, $u=v$,

So, downward velocity of bullet, $v^{\prime }=-v$,

Hence, change in velocity, $\Delta v=v-(-v)=2v$

As, $10$ bullets strike in $1s$,

Therefore, $1$ bullet strikes in $1/10=0.1s$

Hence, upward force by a bullet,

$F_U=m\left(\Delta v/\Delta t\right)$,

$F_U=0.05\left(2v/0.1\right)$,

In balanced state, $F_U=F_D$,

$0.05\left(2v/0.1\right)=0.98$

$v=0.98m/s=98cm/sec$