An object falls from a height of 10 m above the ground. After striking the ground it loses $50 \%$ of its…
An object falls from a height of 10 m above the ground. After striking the ground it loses $50 \%$ of its kinetic energy. The height upto which the object can rebounce from the ground is:
7.5 m
10 m
2.5 m
5 m
Solution
K.E. just before striking the ground $K_1=m g h_1=m g(10)$
K.E. just after striking the ground $=K_1-\frac{50}{100} K_1=\frac{50}{100} K_1=\frac{K_1}{2}=K_2$
Now, $K_2=m g h_2$
$\Rightarrow \frac{K_1}{2}=m g h_2$
$\Rightarrow \frac{m g(10)}{2}=m g h_2 \Rightarrow h_2=5 \mathrm{~m}$