Question

The body losses half of its velocity on penetrating 3 cm in wooden block, then how much will it penetrate more before coming rest.

a) 1 cm

b) 2 cm

c) 3 cm

d) 4 cm

Answer 1

Let $u$ be the initial velocity of the penetrating body. Assume constant retardation inside the wooden block.

Then using the formula $v^2=u^2+2as$.

$v=\frac{u}{2} ,a<0,s=3\;cm$. Substituting,$\frac{u^2}{4}=u^2+2(0.03)a\\ \frac{3u^2}{4(-a)}=0.06\\ \frac{u^2}{(-a)}=0.08$

Let $s'$ total distance penetrated. Then,

$0=u^2+2as'\\ s'=\frac{u^2}{2(-a)}\\ s'=\frac{0.08 }{2}\\ s'=0.04\; m\\ s'=4 \cm$

The extra distance penetrated is $4-3=1\;cm$.

Correct choice is (a).