Question

A steel ball is dropped from a height $h_0$. The collision of the ball with the floor is inelastic with coefficient of restitution e. Then, the height up to which the ball will rise after second collision is :

• A. $e^4{h}_0$
• B. $2e{h}_0$
• C. $e^2{h}_0$
• D. $e^{-2}{h}_0$

Answer 1

Answer: (A)

$e^4{h}_0$

we know that $e=\sqrt{\frac{h^{{}^{\prime }}}{h}}$

therefore height after first collision is $h^{{}^{\prime }}=e^2{h}_o$

now ball will collide second time and will reach a new height which is

$e=\sqrt{\frac{h^{{}^{\prime \prime }}}{h^{{}^{\prime }}}}$

$h^{{}^{\prime \prime }}=e^2{h}^{{}^{\prime }}=e^2\times e^2{h}_o=e^4{h}_o$