An object falls from a height of 10 m above the ground. After striking the ground it loses 50% of its kinetic energy.

Question

An object falls from a height of \(10 \mathrm{~m}\) 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:

(1) \(7.5 \mathrm{~m}\)

(2) \(10 \mathrm{~m}\)

(3) \(2.5 \mathrm{~m}\)

(4) \(5 \mathrm{~m}\)

Answer 1

Correct option is : (4) \(5 \mathrm{~m}\)

K.E. just before striking the ground \(K_{1}=m g h_{1}=m g(10)\)

K.E. just after striking the ground \(=K_{1}-\frac{50}{100} K_{1}=\frac{50}{100} K_{1}=\frac{K_{1}}{2}=K_{2} \)     

\(\text { Now, } K_{2}=m g h_{2} \)

\(\Rightarrow \frac{K_{1}}{2}=m g h_{2} \) 

\( \Rightarrow \frac{m g(10)}{2}=m g h_{2} \Rightarrow h_{2}=5 \mathrm{~m} \)