Question

A bullet of mass m moving with a velocity v 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. $\frac{M + m}{M}\sqrt{2gh}$
• D. $\frac{m}{M + m}\sqrt{2gh}$

Answer 1

Answer: (A)

$\frac{m + M}{m}\sqrt{2gh}$

Answer 2

By the conservation of momentum $mv = (m + M)V$

and if the system goes upto height h then $V = \sqrt{2gh}$

∴ $mv = (m + M)\sqrt{2gh}$ ⇒ $v = \frac{m + M}{m}\sqrt{2gh}$.