Question

A large block of wood of mass $M$ $=5.99\text{kg}$ is hanging from two long massless cords. A bullet of mass $m=10\text{g}$ is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance $h=9.8\text{cm}$ before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (take $g=9.8{\text{ms}}^{-2}$)

• A. $831.4\text{m/s}$
• B. $841.4\text{m/s}$
• C. $811.4\text{m/s}$
• D. $821.4\text{m/s}$

Answer 1

The correct option is A $831.4\text{m/s}$

Let the spped of bullet just before collision is $u$ and speed of (block+bullet) just after collision is $v$.

Using momentum conservation just before and after the collision:
$P_i=0.01\times u+0=P_f=6\times v$
$v=\frac{0.01u}{6}\text{m/s}$

Using energy conservation:
$\frac{1}{2}\times 6\times v^2=6\times g\times h$
$\Rightarrow \frac{1}{2}\times {\left(\frac{0.01u}{6}\right)}^2=9.8\times 9.8\times {10}^{-2}$
$\Rightarrow u=9.8\times 6\sqrt{2}\times 10$
$\therefore u=831.4\text{m/s}$