Question

A bullet of mass $50gm$ is fired from below into a bob of mass $450gm$ of a pendulum. The bullet remains into the bob and the bob rises upto a height $1.8m$. Find $\overrightarrow{V}$ of bullet.

Answer 1

It is given that:

Mass of bullet $=0.05Kg$

Mass of bob $=0.45Kg$

Height of bob and bullet $=1.8m$

Let $V$ be the velocity bullet.

Initial momentum before collision

$=0.05V+0.45\times 0$

$=0.05V$(Initially the bob is at rest)

Let $v$ is the velocity after the impact of both bullet and Bob.

Final momentum after collision is $=(0.05+0.45)v=0.5v$

According to conservation of momentum

$p_i=p_f$

$0.05V=0.5v$

$V=10v.........\left(1\right)$

Now the bullet and bob rises to a height of 1.8 m.

$KE=PE$

$\frac{1}{2}\times 0.05\times V^2=0.05\times 10\times 1.8$

$V^2=36$

$100v^2=6m/s\left(from\right(1\left)\right)$

$v=0.6m/s$

Now put $v$ in equation (1)

$V=10v$

$=10\times 0.6$

$=6m/s$