Question

A bullet fired into a wall loses half of its velocity after penetrating 3 cm. Further it can penetrate a maximum of

• A. 3 cm
• B. 2 cm
• C. 1 cm
• D. 0.5 cm

Answer 1

The correct option is C 1 cm

let the friction force acting on the bullet is F.

Loss of kinetic energy = Work done by friction

$\frac{1}{2}m{v}^2-\left(\frac{1}{2}m\right(\frac{v}{2}{)}^2)=fx$

$\frac{3}{8}m{v}^2=f\times 3\times {10}^{-2}$

$F=\frac{\left(\frac{1}{2}m{v}^2\right)}{(\frac{4}{3}\times 3\times {10}^{-2})}=$ $\frac{\left(\frac{1}{2}m{v}^2\right)}{4\times {10}^{-2}}$

if total Kinetic energy is lost;

$\frac{1}{2}m{v}^2=f{x}_2$

$\left(\frac{1}{2}m{v}^2\right)=$ $\frac{\left(\frac{1}{2}m{v}^2\right)}{4\times {10}^{-2}}{x}_2$

$x_2=4\times {10}^{-2}=4cm$

Hence, bullet penetrates further = $x_2-x=4-3=1cm$