Question

A bullet of mass $0.1$ $\text{kg}$ is fired on a wooden block to pierce through it, but it stops after moving a distance of $50$ $\text{cm}$ into it. If the velocity of bullet before hitting the wood is $10$ $\text{m/s}$ and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is $x$ $\text{N}$. The value of $x$ to the nearest integer is.

Answer 1

Given, mass of the bullet, $m=0.1\text{kg}$
Initial speed of the bullet, $u=10\text{m/s}$
Final speed of the bullet, $v=0\text{m/s}$ after travelling $50\text{cm}=0.5\text{m}$

Since bullet is moving with constant deceleration, we can use:
$v^2=u^2+2as$

$\Rightarrow 0^2={10}^2+2(-a)\times 0.5$

Retardation $\left(a\right)=\frac{100}{2\times 0.5}=100{\text{m/s}}^2$

Retarding force $\left(F\right)=ma=0.1\times 100=10\text{N}$