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  • A ball is dropped onto a floor from a height of 10 m. If 15% of its initial energy is lost, then the height of bounce is   Option:

A ball is dropped onto a floor from a height of 10 m. If 15% of its initial energy is lost, then the height of bounce is 

 

Option: 1

2 m

 


Option: 2

4 m

 


Option: 3

8.5 m

 

 


Option: 4

6.4 m


Answers (1)

best_answer

When the ball is dropped from a height of 10 m, its initial potential energy is given by:

P E_i=m g h

where m is the mass of the ball, g is the acceleration due to gravity, and h is the initial height from which it is dropped. When the ball hits the ground, some of its energy is lost due to various factors such as deformation of the ball and air resistance. Here 15% of the initial energy is lost. Therefore, the remaining energy after the bounce is:

P E_f=(1-0.15) P E_i=0.85 \mathrm{mgh}

At the maximum height of the bounce, all the remaining energy is converted into potential energy, which is given by:

P E_f=m g h^{\prime}

where h' is the height of the bounce. Equating the above two equations, we get:

0.85 m g h =m g h^{'}

\\ h^{'} =0.85 h

Substituting  h = 10 m, we get:

h^{\prime}=0.85 \times 10 m=8.5 \mathrm{~m}

Therefore, the height of the bounce is 8.5 m, which corresponds to option (c).

Posted by

Gaurav

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