Question

What is the expression for potential energy?

Answer 1

Hint: We know that potential energy is equivalent to the work done against the gravitational force. So first find the expression for the work done that is $w = mgh$, then equate it to the potential energy to get the final expression that is $PE = mgh$.

Complete Step-by-Step solution:
Potential energy is the energy possessed by a body because of its position relative to other bodies. Gravitational potential energy is the energy held by a body when it is at some height relative to the zero potential level ground. 
When something is elevated above the ground, work needs to be done against the gravitational force. And as the work is done an equivalent amount of energy is transferred to the body due to conservation of energy and it obtains gravitational potential energy as shown in figure 1. If the body falls from the height, an equivalent amount of work has to be done by the gravitational force to bring it back to the ground.

Figure 1

Let us assume the work done against the gravitational force be \[ = w\]
We know $w = Force \times Height $$ = Force \times h$------------------------- (1)

And we also know $Force = mass \times g = mg$------------------------- (2)

Here, $g$ is a gravitational constant whose value is equal to 9.8
Substituting equation (2) in equation (1) we obtain
$w = mg \times h = mgh$----------------------------------------- (3)

So, we get work done equal to $mgh$, and since an equivalent amount of energy is transferred to the body.
The required expression for the potential energy is
$PE = mgh$

Note: For these types of questions, we use the basic concept of conservation of energy. We first find the expression for work done and then equate it to the energy or vice versa. We can also equate two different types of energy when needed.