Question

A bullet of mass 50 g is fired from below into the bob of mass 450 g of a long simple pendulum as shown in figure. The bullet remains inside the bob and the bob rises through a height of 1.8 m. Find the speed of the bullet. Take g = 10 $m/s^2$.

• A. 60 m/s
• B. 120 m/s
• C. 50 m/s
• D. 70 m/s

Answer 1

The correct option is A 60 m/s

Let the speed of the bullet be $v$. Let the common velocity of the bullet and the bob, after the bullet is embedded into the bob, is $V$. By the principle of conservation of the linear momentum,

$V=\frac{\left(0.05kg\right)v}{0.45kg+0.05kg}=\frac{v}{10}$

The string becomes loose and the bob will go up with an acceleration of $g=9.8m/s^2$. As it comes to rest at a height of $1.8m$, using the equation $v^2=u^2+2ax$,

$1.8m=\frac{(v/10{)}^2}{2\times 10m/s^2}$

or $v=60m/s$.

Hence, the speed of the bullet is $60m/s$