From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m/s. Calculate the initial recoil velocity of the rifle.

Given, mass of bullet( \( m_1 \) ) = 50 g

Mass of rifle( \( m_2 \) ) = 4000 g

Initial velocity of the fired bullet( \( v_1 \) ) = 35 m/s

Let the recoil velocity be \( v_2 \).

Since the rifle was initially at rest, the initial momentum of the rifle = 0

Total momentum of the rifle and bullet after firing = \( m_1 v_1 + m_2 v_2 \)

Now we know that, the total momentum of the rifle and the bullet after firing = 0
{ By law of conservation of momentum}

\( \therefore m_1 v_1 + m_2 v_2 \) = 0
\( \Rightarrow v_2 = - \frac{m_1 v_1}{m_2} \)

= - \frac{50 × 35}{4000} = -0.4375 m/s