Question

A bullet of mass m moving with a velocity $v_1$ strikes a suspended wooden block of mass M as shown in the figure and sticks to it. If the block rises to a height h the initial velocity of the bullet is-

• A. $\frac{m+M}{m}\sqrt{2gh}$
• B. $\sqrt{2gh}$
• C. $\frac{M+m}{m}\sqrt{gh}$
• D. $\frac{m}{M+m}\sqrt{2gh}$

Answer 1

The correct option is A $\frac{m+M}{m}\sqrt{2gh}$

From the conservation of momentum
$(m+M)v^{\prime }=m{v}_1$
$v^{\prime }=\frac{m{v}_1}{m+M}$ ......(i)
Now from conservation of energy
$\frac{1}{2}(m+M)v^{\prime 2}=(m+M)gh$
$\therefore v^{\prime }=\sqrt{2gh}$ ........(ii)
from equation (i) and (ii) $v_1=\frac{M+m}{m}\sqrt{2gh}$