Question

A $30g$ bullet travelling initially at $500m/s$ penetrates $12cm$ into a wooden block. The average force exerted will be
(A) $31250N$
(B) $41250N$
(C) $31750N$
(D) $30450N$

Answer 1

Hint
First we have to calculate the kinetic energy of the bullet and then using the work-energy theorem we can substitute suitable values in the formula and calculate the average force exerted by the bullet.
$\Rightarrow K = \dfrac{1}{2}m{v^2}$ where $K$ is the kinetic energy, $m$ is the mass of the bullet and $v$ is its velocity.
$\Rightarrow W = F \times d$ where $W$ is the work done and $d$ is the distance travelled.

Complete step by step answer
Here we have a bullet which has a mass of $30g$. Its velocity is $500m/s$ which means that it is travelling a distance of $500m$ in $1s$.
Since the bullet is in motion so it must possess kinetic energy. Kinetic energy is the energy that a body possesses by the virtue of its motion.
So first let us calculate the value of the kinetic energy of the bullet.
The formula for kinetic energy is,
$\Rightarrow K = \dfrac{1}{2}m{v^2}$
$\Rightarrow K = \dfrac{1}{2} \times 30 \times {10^{ - 3}} \times {500^2}$
$\Rightarrow K = 3750J$
It penetrates $12cm$ into a wooden block so we can calculate the work done by the bullet using the formula $W = F \times d$ where $W$ is the work done, $F$ is the force exerted and $d$ is the distance travelled.
Here, we apply the work-energy theorem which states that the net work done by the forces on an object is equal to the change in its kinetic energy.
Therefore, $W = K$
Substituting the values in this equation we get,
$\Rightarrow 3750 = F \times 12 \times {10^{ - 2}}$
$\Rightarrow F = \dfrac{{3750}}{{12 \times {{10}^{ - 2}}}}$
$\Rightarrow F = 31250N$
Therefore, the correct option is (A).

Note
The values of all the quantities must be in the same unit. Here as the answer given is in SI unit, so all the quantities must be converted into SI units as well.