Question

If a body loses half of its velocity on penetrating $3$ cm in a wooden block, then how much will it penetrate more before coming to rest

• A. $1cm$
• B. $2cm$
• C. $3cm$
• D. $4cm$

Answer 1

The correct option is A $1cm$

Let initial velocity be $v$.
Initial Energy $=\frac{1}{2}m{v}^2$

Final energy $=\frac{1}{2}m(\frac{v}{2}{)}^2=\frac{1}{4}(\frac{1}{2}m{v}^2)$

Energy lost $=\frac{1}{2}m{v}^2-\frac{1}{4}\left(\frac{1}{2}m{v}^2\right)$$=\frac{3}{4}\left(\frac{1}{2}m{v}^2\right),------\left(for3cm\right)$

So, Remaining energy $=\frac{1}{4}\left(\frac{1}{2}m{v}^2\right)$

Using unitary method,

$\frac{3}{4}\left(\frac{1}{2}m{v}^2\right)\to 3cm$ penetration

$\Rightarrow \frac{1}{4}\left(\frac{1}{2}m{v}^2\right)\to 1cm$ penetration