Question

A bullet of mass $50g$ moving horizontally with a velocity $210{ms}^{-1}$ gets embedded in a block of mass $1kg$ kept on a rough horizontal surface. If the coefficient of kinetic friction between the block and the surface is $0.5$, the block-bullet system will move a distance of ____________ before coming to rest. (Acceleration due to gravity $=10{ms}^{-2}$)

• A. $40m$
• B. $30m$
• C. $20m$
• D. $10m$

Answer 1

Answer: (D)

$10m$

Collision is completely inelastic as the bullet and the block are moving together. By conservation of momentum
$mu=(M+m)v\Rightarrow v=\frac{mu}{M+m}=\frac{0.05\times 210}{1.05}=10m/saccelerationbecauseofkineticfrictionis-0.5g=-5m/s^{2}s=\frac{-u^2}{2a}=\frac{100}{10}=10m$