Question

A ball of mass 10 gram is dropped from a height of hundred metre, after striking the ground 25% of kinetic energy decreases. how much height the ball will attend after striking the ground?​

Answer 1

By energy conservation, the kinetic energy of the ball when it hits the ground is equal to its potential energy at the height where the ball is dropped.

[The ball has no kinetic energy at the height where it is dropped, and no potential energy at ground.]

That is,

$\sf{\longrightarrow KE=mgh}$

Here,

• $\sf{m=0.01\ kg}$

• $\sf{h=100\ m}$

Let $\sf{g=10\ m\,s^{-2}.}$ Then,

$\sf{\longrightarrow KE=0.01\times10\times100}$

$\sf{\longrightarrow KE=10\ J}$

After striking the ground the kinetic energy gets reduced by 25%. So the new kinetic energy becomes,

$\sf{\longrightarrow KE=10\times\dfrac{75}{100}}$

$\sf{\longrightarrow KE=7.5\ J}$

This is equal to the potential energy at the height till which the ball rebounds, i.e.,

$\sf{\longrightarrow mgh'=7.5}$

$\sf{\longrightarrow 0.01\times10h'=7.5}$

$\sf{\longrightarrow 0.1h'=7.5}$

$\sf{\longrightarrow\underline{\underline{h'=75\ m}}}$

Hence the ball will rise by 75 m after striking the ground.

Answer 2

Given,

• M = 10g = 0.01kg
• h = 100m
• After striking the ground 25% of kinetic energy decreases.

To Find,

• How much height the ball will attend after striking the ground?

Solution,

$:\implies Kinetic \: \: Energy = Mgh \: \: (g = 10m {s}^{ - 2} ) \\ \\ :\implies Kinetic \: \: Energy = 0.01kg \times 10m {s}^{ - 2} \times 100m \\ \\ :\implies Kinetic \: \: Energy = 10J$

After striking the ground 25% of kinetic energy decreases.

So,

75% of Kinetic Energy remains

$:\implies 75 \: percent \: \: of \: \: 10J \\ \\ :\implies \frac{75}{100} \times 10J \\ \\:\implies 7.5J$

Required Answer,

$:\implies Kinetic \: \: Energy = 7.5J \\ \\:\implies Mgh = 7.5J \\ \\:\implies 0.01kg \times 10m {s}^{ - 2} \times h = 7.5J \\ \\:\implies 0.1kgm {s}^{ - 2} \times h = 7.5J \\ \\ :\implies h = \frac{7.5J}{0.1kgm {s}^{ - 2} } \\ \\ :\implies h = 75m$

Height = 75m