Question

Shyam drops a ball of \[100\,g\] from a building of height \[10\,m\]. What will be its kinetic energy at the height of \[4\,m\]? What will happen to its total mechanical energy? Give reasons to justify your answer.

Answer 1

Hint: Find the Velocity and then substitute its value in the formula of K.E to get the value of the Kinetic Energy.
As the height decreases its potential energy is transformed to kinetic energy.

Complete step by step answer:
Total Height of the building \[ = 10\,m\]
Mass of the Ball \[ = 100\,g = 0.1\,kg\]
The ball is dropped from the building and at a height of 4m, that is the ball travels \[(10 - 4)m\, = \,6m\] from the top of the building after dropping.
At this point of height, velocity of the ball
\[{v^2} = {u^2} + 2gs\]
$\implies$ \[{v^2} = 0 + 2 \times 10 \times 6\] [Here, u=0 as it starts from rest]
$\implies$ \[{v^2} = 120\]
We know that,
Kinetic Energy (K.E)= \[\dfrac{1}{2}m{v^2}\]
 = \[\dfrac{1}{2} \times 0.1 \times 120\]
 = \[6J\]

So, the correct answer is “6J”.

Additional Information:
Total mechanical energy of a body is the summation of its potential energy and kinetic energy which remains constant.
In this case, as the height decreases its potential energy is transformed to kinetic energy. But the total mechanical energy is conserved.
Potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
The formula for potential energy depends on the force acting on the two objects. For the gravitational force the formula is:
\[W = mgh\]
Where,
m is the mass in kilograms
g is the acceleration due to gravity
h is the height in meters
Kinetic Energy- It is defined as the energy of an object because of its motion or the energy gained by an object from its state of rest to motion.

Note:
Kinetic energy is due to an object’s motion whereas potential energy is due to an object’s position or state. Velocity is an important factor while calculating an object’s kinetic energy. However, velocity has nothing to do with an object’s potential energy.