Question

A ball is dropped from a height of 10m. If 40% of its energy is lost on collision with the earth then, after the collision the ball will rebound to a height of:
A- 10 M
B- 8 M
C- 4 M
D- 6 M

Answer 1

Hint: since the ball is just dropped from a certain height so, its initial velocity is zero. Initially it is at some height so it possesses only gravitational potential energy. We can use Newton's equations of motion to find the velocity of the ball when it hits the ground. Energy at the ground will be purely kinetic energy.

Complete step by step answer:
Initial velocity, u= 0 m/s
Final velocity, v=?
Distance covered, s= 10 m
Finding out the initial energy at the height, \[U=mgh\]
\[\begin{align}
  & \Rightarrow U=m\times 10\times 10 \\
 & \Rightarrow U=100mJ \\
\end{align}\]
Since there is no air friction present, so no energy is lost and at the collision 40% energy is lost, so, energy left will be
\[\begin{align}
  & 100m-\dfrac{40}{100}\times 100m \\
 & \Rightarrow 100m-40m \\
 & \therefore 60mJ \\
\end{align}\]
Now it has 60m J of energy left and it rebounds back, let us assume the height reached is x metres.
\[\begin{align}
  & \Rightarrow mgx=60m \\
 & \Rightarrow x=\dfrac{60}{10} \\
 & \therefore x=6m \\
\end{align}\]
Hence the ball will bounce back to a height of 6m.

So, the correct answer is “Option D”.


Note:
Work energy theorem states that work done is equal to the change in the potential energy of the object. We can also make use of work energy theorem to find out the final velocity of the object when it hits the ground. Here U=100m J does not mean mili Joule but m is the mass of the body which has dropped from a certain height.