A `20 ` gm 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 , it is found that the two plates initily atrest , now move with equal velocity . Find the percentage loss in the initial velocity of the bullet when it is between `M` and `M_(2)` neglet any loss of material of the pletes due to the action of the bullet

Options

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

Answer

B

Explanation

Apply conservation of momemntum after piercing `M_(1): m u = m_(1)v + m u_(1)` (i)
After it enters into `M_(2)`, finally bullet also moves with velocity `v`, so `m u_(1) = (M_(2)+m)v` (ii)
From (i) and (ii), we get `m u = (M_(1)+M_(2)+m)v` (iii)
Required percentage loss
`= (u-u_(1))/(u) xx 100 = (m(u-u_(1)))/(m u) xx 100`
`= (M_(1)v)/((M_(1) +M_(2)+m)) xx 100 = (1)/(1+2.98+0.02) xx 100 = 25%`