Question

A body of mass 500gm is rotating in a vertical circle of radius 1m. What is the difference in its kinetic energies at the top and bottom of the circle?
(A) $4.9J$
(B) $19.8J$
(C) $2.8J$
(D) $9.8J$

Answer 1

Hint: To find the difference in kinetic energies at top and bottom of the circle we need to know the relation between kinetic energy and work done. This relation is given by Work-Energy Theorem. Using that relation, we need to find the difference in the kinetic energy in the top and bottom of the circle.

Formula used:
In this solution we will be using the following formula,
$\Rightarrow \Delta K.E = W$
$\Rightarrow W = mg(2r)$
Where, $W$ is the work done and $K.E$ is the kinetic energy of the body, $m$ is the mass of the body, $g$ is the acceleration due to gravity, $r$ is the radius of the circle.

Complete step by step solution:
Let us understand the statement of Work-Energy Theorem. It states that the net work done by the forces on an object equals the change in its kinetic energy.
$\Rightarrow \Delta K.E = W$
Where, $W$ is the work done and $K.E$ is the kinetic energy of the body.
To find out the difference in the kinetic energies at the top and the bottom of the circle, we need to find the work done by the body. It gives us the change in the kinetic energies of the object while it was in the top of the circle and bottom of the circle.
Thus, the work done by the body is given by,
$\Rightarrow W = mg(2r)$
Where, $m$ is the mass of the body, $g$ is the acceleration due to gravity, $r$ is the radius of the circle.
As given in the question, $m = 500gm$, $r = 1m$ and $g = 9.8m/{s^2}$ when we substitute the values of the given variables, we get,
$\Rightarrow W = 0.5 \times 9.8 \times (2 \times 1)$
On calculating we get
$\Rightarrow W = 9.8J$
Thus, the difference in the kinetic energies of the body when it was in the top and the bottom is equal to 9.8 J.
Hence, the correct option is (D).

Note:
The Work-Energy theorem is very useful in analyzing situations where a rigid body moves under several forces. Thus, the work done by any force acting on a rigid body is equal to the change in its kinetic energy. This is the basis of the work energy equation for rigid bodies.