Question

A wooden block of mass M is suspended by a cord and is at rest. A bullet of mass m, moving with a velocity v pierces through the block and comes out with a velocity $v/2$ in the same direction. If there is no loss in kinetic energy, then upto what height the block will rise A wooden block of mass M is suspended by a cord and is at rest. A bullet of mass m, moving with a velocity v pierces through the block and comes out with a velocity $v/2$ in the same direction. If there is no loss in kinetic energy, then upto what height the block will rise

• A. $m^{2}v^{2}/2M^{2}g$
• B. $m^{2}v^{2}/8M^{2}g$
• C. $m^{2}v^{2}/4Mg$
• D. $m^{2}v^{2}/2Mg$

Answer 1

Answer: (B)

$m^{2}v^{2}/8M^{2}g$

Answer 2

By the conservation of momentum

Initial momentum = Final momentum

$mv + M \times 0 = m\frac{v}{2} + M \times V$ ⇒ $V = \frac{m}{2M}v$

If block rises upto height h then

$h = \frac{V^{2}}{2g} = \frac{(mv/2M)^{2}}{2g} = \frac{m^{2}v^{2}}{8M^{2}g}$.