Question

From a rifle of mass $4kg$, a bullet of mass $50g$ is fired with a velocity of $35{ms}^{-1}$​ with respect to the ground. Calculate the recoil velocity of the rifle.

• A. $1{ms}^{-1}$​
• B. $0.4375{ms}^{-1}$​
• C. $0{ms}^{-1}$​
• D. $2.5{ms}^{-1}$​

Answer 1

The correct option is B

$0.4375{ms}^{-1}$​

Let initial velocity of bullet be $u_1$ and initial velocity of rifle be $u_2$.
$u_1=u_2=0$ (Initially bullet and rifle system was at rest)
Let, mass of rifle ,$m_1$ = $4kg$

Mass of bullet, $m_2$ = $\frac{50}{1000}=0.05kg$

Final velocity of bullet, $v_2$ = $35{ms}^{-1}$​
Final velocity of rifle, $v_1$ = v

From principle of conservation of linear momentum:
Initial momentum is equal to final momentum.
$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
$4\times 0+0.05\times 0=4\times v+0.05\times 35$
$0=1.75+4v$
$\Rightarrow$$v=-0.4375m{s}^{-1}$

The negative sign indicates that the rifle recoils in the opposite direction with the velocity of $0.4375{ms}^{-1}$.