Question

A bullet of mass $50g$ if fired from below into the bob of mass $450g$ of a long simple pendulum as shown in Fig. The bullet remains inside the bob and the bob rises through a height of $1.8m$. Find the speed of the bullet.

Answer 1

Let the speed of the bullet be $\nu$. Let the common velocity of the bullet and the bob, after the bullet is embedded into the bob, be $V$. By the principle of conservation of linear momentum,
$V=\frac{\left(0/05kg\right)\nu }{0.45kg+0.05kg}=\frac{\nu }{10}$
The string loose and the bob will go up with a deceleration of $g=10m/s^2$. As it comes to rest at a height of $1.8m$, using the equation ${\nu }^2+2ax$, we get
$1.8m=\frac{{\left(\frac{\nu }{10}\right)}^2}{2\times 10m/s^2}$ or $\nu =60ms$.