A bullet of mass $m$ is fired from a rifle of mass $M$. If $\mathbf{v}$ be the velocity of the bullet,…
A bullet of mass $m$ is fired from a rifle of mass $M$. If $\mathbf{v}$ be the velocity of the bullet, velocity acquired by the rifle is
$\mathbf{v}_r=\frac{-M}{m} \mathbf{v}$
$\mathbf{v}_r=\frac{-m}{M} \mathbf{v}$
$\mathbf{v}_r=-\mathbf{v}$
$\mathbf{v}_r=+\mathbf{v}$
Solution
Given that, mass of bullet $=m$
Mass of rifle $=M$
Velocity of bullet $=\mathbf{v}$
Let velocity of rifle $=\mathbf{v}_r$
By using conservation of linear momentum
$m \mathbf{v}+M \mathbf{v}_r=0$ $[\because$ Initial momentum of bullet and rifle was zero]
$\therefore \quad \mathbf{v}_r=\frac{-m \mathbf{v}}{M}$
Here - ve sign shows that velocity of rifle is opposite to the velocity of bullet.