Question

A bullet moving with a velocity of 300 m/s is just able to pierce a block of wood 20 cm thick. If it is required to pierce a block of wood 18 cm thick, its velocity should be

• A. $90$ $m{s}^{-1}$
• B. $284.6$ $m{s}^{-1}$
• C. $900$ $m{s}^{-1}$
• D. $9$ $m{s}^{-1}$

Answer 1

The correct option is C $900$ $m{s}^{-1}$

Kinetic energy (KE) of bullet = work done by friction force

let friction force be F.

assuming F is same in both cases, we have

$\begin{array}{c}\frac{1}{2}m{v}_1^2=F.s_1=s_1\times F............\left(1\right)\\ \&\frac{1}{2}m{v}_2^2=F.s_2...............\left(2\right)\\ Where\\ V_1=300m/s;v_2=?\\ s_1=2cm;s_2=18cm\\ dividing\left(2\right)by\left(1\right)\\ \frac{v_2^2}{v_1^2}=\frac{s_2}{s_1}\\ \Rightarrow v_2=\left(\sqrt{\frac{s_2}{s_1}}\right)v_1\\ =\sqrt{\frac{18}{2}}\times 300\\ =900m/s\end{array}$