Question

A $20g$ bullet passes through a plate of mass $1kg$ and finally comes to rest inside another plate of mass $2980g$. It makes the plates move from rest to same velocity. The percentage loss in velocity of bullet between the plate is:

• A. $0$
• B. $50$%
• C. $75$%
• D. $25$%

Answer 1

The correct option is D $25$%

Using conservation of momentum

$0.02u=0.02v+1V_1$ (i)

(where $V_1$ be the velocity of plate of $1kg$)

and $0.02v=(2.98+0.02)V_1$ (ii)

($\because$ plate of $3kg$ has also same velocity i.e. $V_1$)

or $V_1=0.02\frac{v}{3}$

Substituting

$\therefore 0.02u=0.02v+0.02\frac{v}{3}$

or $u=\frac{4v}{3}$ or $v=\frac{3}{4}u$

percentage loss in velocity $=|\frac{u-v}{u}|\times 100$

$=|\frac{u-\frac{3}{4}u}{u}|\times 100=25$%