Question

From a rifle of mass 4 kg, a bullet of mass 50 g is fired with a velocity of $35m{s}^{-1}$.The recoil velocity of the rifle is:

• A. 0.3375 m/s
• B. 0.4375 m/s
• C. 0.4 m/s
• D. 0 m/s

Answer 1

The correct option is B

0.4375 m/s

Given, mass of rifle ($m_1$) = 4 kg, initial velocity of rifle ($u_1$) = initial velocity of bullet ($u_1$) = $0m{s}^{-1}$

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

Final velocity of bullet ($v_2$) = $35m{s}^{-1}$
Let final velocity of rifle or recoil velocity of rifle = ($v_1$)

Since momentum is conserved, so initial momentum is equal to final momentum

$4\times v_1$ + $35\times 0.05$ = 0
$v_1$ = $\frac{-35\times 0.05}{4}$
$v_1=-0.4375m{s}^{-1}$

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