Question

A rubber ball of mass 50$g$ falls from a height of $m$ and rebounds to a height of .5$m$ . The impulse between the ball and the ground if the time during which they are in contact was $0,1$ sec is

• A. $12.5N-s$
• B. $11.8N-s$
• C. $2.36N-s$
• D. $3.76N-s$

Answer 1

The correct option is D $3.76N-s$

Given,

mass of ball is $50g$

Height is $1m$

Rebound at height $0.5m$

When ball is falling from height $1m$ then initial velocity will be zero. when it strike on ground then Final velocity is ,

$v^2=u^2+2gh{v}^2=0^2+2\times 9.8\times 1v=\sqrt{19.6}v=4.4m/s$

Now when ball rebound then final velocity will be zero therefore initial velocity is

$v^2=u^2-2gh{0}^2=u^2-2\times 9.8\times 0.5u=\sqrt{9.8}u=3.13m/s$

Time of contact$\left(t\right)$ is $0.1sec$

Impulse is change in momentum

$I=m(v-u)I=\frac{50}{1000}(4.4-(-3.13\left)\right)I=\frac{50}{1000}(4.4+3.13)I=0.376N-s$

Force exerted is $F=\frac{0.376}{0.1}=3.76N$