Question

5 bullets, each of mass 10 gm are fired per second, vertically upwards, such that a plate of mass 200 gm floats in air. If the bullets rebound with the same velocity back vertically downwards, the velocity with which each bullet is fired in ms${}^{-1}$ is:
(Take $g=10m{s}^{-2}$)

• A. 10
• B. 30
• C. 20
• D. 40

Answer 1

The correct option is C 20

We know that,

$F=\frac{dp}{dt}$

$\Rightarrow dp=Fdt$

The change in momentum $dp$ is given by,

$dp=m|v_f-u_i|$

$\Rightarrow dp=nm|v-(-v)|=2nmv$

Here, $n=5,m=10$gm$=0.01$kg.

$\Rightarrow dp=2\left(5\right)\left(0.01\right)v=0.1v$ kgm/s

$\therefore Fdt=dp$

$\Rightarrow mgdt=dp$

$\Rightarrow \left(0.2\right)\left(10\right)=0.1v$

$\Rightarrow 2=0.1v$

$\Rightarrow v=\frac{2}{0.1}=20m/s$