Question

A bullet of mass $50\text{g}$ is fired horizontally into a wooden block of mass $10\text{kg}$. The bullet penetrates the wooden block and moves through a distance of $5\text{m}$ before coming to a stop within the block. If the initial speed of the bullet is $100\text{m/s}$, then what is the deceleration of the bullet? (Assume retarding force is uniform)

• A. $250{\text{m/s}}^2$
• B. $100{\text{m/s}}^2$
• C. $500{\text{m/s}}^2$
• D. $1000{\text{m/s}}^2$

Answer 1

The correct option is D $1000{\text{m/s}}^2$

Initial speed of the bullet,$u=100m/s$
$\therefore$ Kinetic energy of the bullet, $KE=\frac{1}{2}m{v}^2=\frac{1}{2}\times 0.05\times {100}^2\Rightarrow KE=250J$

The block does work on the bullet to stop it. The work done by the block on the bullet is given by,
$W=Fs$ where $F$ is the uniform retarding force and
$s=5\text{m}$ (given)

By Work Energy Theorem,
Work done by the block = initial kinetic energy of the bullet
Therefore, we get,
$-Fs=-5F=250$
$\Rightarrow F=-50\text{N}$

Therefore uniform retardation of the block is
$a=\frac{F}{\text{mass of bullet}}$
$=\frac{-50}{0.05}=-1000{\text{m/s}}^2$
(-ve sign due to retardation)