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

$u=u_{0}V=\frac{u_0}{2}S=3cm{V}^2-u^2=2as\Rightarrow \frac{u_0^2}{4}-u_0^2=2a3\Rightarrow \frac{{-3u}_0^2}{4}=2a3\Rightarrow a=\frac{{-u}_0^2}{8}Nowu=\frac{u_0}{4}V=0a=\frac{{-u}_0^2}{8}S=?V^2-u^2=2as\Rightarrow 0^2-\frac{u_0^2}{4}=2\left(\frac{{-u}_0^2}{8}\right)\times S\Rightarrow \frac{1}{4}=\frac{S}{4}S=1cm$