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Answer :
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