A ball of mass M falls from a height h on a floor and its coefficient of restitution is e. The height attained by the ball after two rebounds is

Question

A ball of mass M falls from a height h on a floor and its coefficient of restitution is e. The height attained by the ball after two rebounds is (A) e2h (B) eh2 (C) e4h (D) (h/e4)

Tardigrade Admin · Accepted Answer

A ball falling from height h reaches the floor with velocity

v = 2 g h

By definition

e = \frac{velocity of separation}{velocity of approach}

∴

Rebound velocity

= e 2 g h

∴

Rebound height

= e^{2} h

After two rebounds, height

= e^{4} h

Q. A ball of mass $M$ falls from a height h on a floor and its coefficient of restitution is $e$ . The height attained by the ball after two rebounds is

$e^{2} h$

$e h^{2}$

$e^{4} h$

$\frac{h}{e ^{4}}$

A ball falling from height h reaches the floor with velocity
$v = 2 g h$
By definition
$e = \frac{velocity of separation}{velocity of approach}$
$∴$ Rebound velocity $= e 2 g h$
$∴$ Rebound height $= e^{2} h$
After two rebounds, height $= e^{4} h$

Q. A ball of mass M falls from a height h on a floor and its coefficient of restitution is e. The height attained by the ball after two rebounds is

e2h

eh2

e4h

e4h​