Question

An 8 gm bullet is fired horizontally into a 9 kg block of wood and sticks in it. The block which is free to move, has a velocity of 40 cm/s after impact. The initial velocity of the bullet is

• A. 450 m/s
• B. 450 cm/s
• C. 220 m/s
• D. 220 cm/s

Answer 1

The correct option is A 450 m/s

By using momentum conservation, we get,

$m_1{u}_1+m_2{u}_2=(m_1+m_2)V$

$\Rightarrow V=\frac{m_1{u}_1+m_2{u}_2}{m_1+m_2}$

But $m_1=8$ gm$,m_2=9000$gm$,u_2=0$cms${}^{-1},V=40$cm${}^{-1},u_1=?$

$\Rightarrow 40=\frac{8u_1+9\left(0\right)}{8+9000}$

$\Rightarrow u_1=\frac{40}{8}\left(9008\right)=45040$cms${}^{-1}\approx 450$ms${}^{-1}$