Question

A ball of mass 50 gm is dropped from a height h = 10 m. It rebounds losing 75 percent of its kinetic energy. If it remains in contact with the ground for At =0.01 sec, the impulse of the impact force is
(take 9 = 10 $m/s^2$)

• A. 1.3 N - s
• B. 1.06 N - s
• C. 1300 N - s
• D. 105 N - s

Answer 1

The correct option is B 1.06 N - s

Given : $m=0.05$ kg $h=10$ m

Kinetic energy of ball just before collision $E_i=mgh=0.05\times 10\times 10=5$ J

Thus initial momentum of the ball $P_i=\sqrt{2m{E}_i}=\sqrt{2\left(0.05\right)\left(5\right)}=0.707$ N-s (downwards)

Kinetic energy of ball just after collision $E_f=\frac{E_i}{4}=\frac{5}{4}=1.25$ J

Thus final momentum of the ball $P_f=\sqrt{2m{E}_f}=\sqrt{2\left(0.05\right)\left(1.25\right)}=0.353$ N-s (upwards)

$\therefore$ Impulse $I=\Delta P=P_f-(-P_i)=0.353+0.707=1.06$ N-s