Question

A ball of mass $400gm$ is dropped from a height of $5m$. A boy on the ground hits the ball vertically upwards with a bat with an average force of $100N$ so that it attains a vertical height of $20m$. Find the time for which the ball remains in contact with the bat.

• A. $0.12s$
• B. $0.24s$
• C. $0.36s$
• D. $0.48s$

Answer 1

The correct option is A $0.12s$

$M=0.4gm$ $=0.4kg$

$h_1=5m$ $,$ $h_2=20m$

$g=10m/s^2$

Velocity of the ball after dropping $5m:u$

Velocity of the ball after being hit by the bat$:v$

$u^2=2g{h}_1;u=\sqrt{\left(2\times 10\times 5\right)}=10m/s\left(downwards\right)$

$v^2=2g{h}_2;\left(2\times 10\times 20\right)=v=20m/s\left(upwards\right)$

Change of momentum $=$impulse$=$ $m(v+u)=12kgm/s$

Force$=100N=12/t$

$t=$ time of contact $=0.12sec$

Hence,

option $\left(A\right)$ is correct answer.