Question

The bag of sand of mass 2 kg is suspended by a rope. A bullet of mass 10 g is fired at it and gets embedded into it. The bag rises up a vertical height of 10 cm. The initial velocity of the bullet is nearly:

• A. 70 m/s
• B. 140 m/s
• C. 210 m/s
• D. 281 m/s

Answer 1

The correct option is D 281 m/s

Mass of system M=2+0.01=2.01 Kg

Let the velocity after bullet embedded into sand bag be v

$\frac{M{v}^2}{2}=Mgh\Rightarrow v=\sqrt{2gh}=\sqrt{2\times 9.8\times 0.1}=1.4m/s$,

$h=10cmor0.1m$

Lets say the velocity of bullet be $V$

Then by momentum conservation $mV=Mv\Rightarrow 0.01\times V=2.01\times 1.4$

So $V=281m/s$