Question

A $10gm$ bullet moving directly upward at $1000m/s$ strikes and passes through the center of mass of a $10kg$ block initially at rest. The bullet emerges from the block moving directly upward at $400m/s$. What will be velocity of the block just after the bullet comes out of it?

• A. $1m/s$
• B. $0.4m/s$
• C. $1.4m/s$
• D. $0.6m/s$

Answer 1

The correct option is D $0.6m/s$

Given,
Weight of bullet $\left(m_B\right)=10gm$
$=10\times {10}^{-3}kg$
Weight of block $\left(M\right)=10kg$
Initial velocity of bullet $\left(v_i\right)=1000m/s$
Final velocity of bullet $\left(v_f\right)=400m/s$
By the law of conservation of momentum,
$m_B{V}_i=m_B{V}_f+10V$
[where, $v=$ velocity of block]
$(10\times {10}^{-3})\left(1000\right)=(10\times {10}^{-3})\left(400\right)+10v$
$10=4+10v$
$10v=10-4$
$v=\frac{6}{10}=0.6m/s$.