A `20 g` bullet pierces through a plate of mass `M_(1) = 1 kg` and then comes to rest inside a second plate of mass `M_(2) = 2.98 kg` as shown in Fig. It is found that the two plates, initially at rest, now move with equal velocities. Find the percentage loss in the initial velocity of the bullet when it is between `M_(1)` and `M_(2`. Neglect any loss of material of the plates due to the action of bullet.

Options

A. `50%`
B. `25%`
C. `100%`
D. `75%`

Answer

B

Explanation

Apply conservation of momentum after piercing `M_(1)`:
`"mu"=M_(1)mv+"mu"v_(1)`………i
After it enters into `M_(2)`, finally bullet also moves with velocity `v`, so
`"mu"v_(1=(M_(2)=m)v`……ii
From i and ii, we get
`"mu"=(M_(1)+M_(2)+m)v`..........iii
Required percentage loss
`=(u-u_(1))/uxx100=(m(u-u_(1)))/("mu")xx100`
`(M_(1)v)/((M_(1)+M_(2)+m)v)xx100`
`=1/(1+2.98+0.02)xx100=25%`