Question

A ball falls on the ground from a height $h_1$ and rebounds to a height of $h_2$. Then, the fractional loss in its kinetic energy during the collision with the ground is :

• A. $\frac{h_1-h_2}{h_1}$
• B. $\frac{h_1-h_2}{h_2}$
• C. $\frac{h_2}{h_1}$
• D. $\sqrt{\frac{h_1-h_2}{h_1}}$

Answer 1

Answer: (A)

$\frac{h_1-h_2}{h_1}$

since all the kinetic energy of ball in the air is lost into its P.E. at its peak.
so we can compare their K.E. by their P.E. at highest point.
initial K.E. $=mg{h}_1$
final K.E. $=mg{h}_2$
fractional loss in K.E.$=\frac{mg{h}_1-mg{h}_2}{mg{h}_1}=\frac{h_1-h_2}{h_1}$