Question

Define potential energy. Derive an expression for gravitational potential energy. Mention its units.

Answer 1

Potential energy is held by an object with respect to the position of another object within itself. The gravitational potential energy is possessed by an object when the work is done on the object against the acceleration due to gravity while lifting the object. The units of gravitational potential energy will be equal to units of energy.

Complete answer:
Potential energy of an object is the energy possessed by the object by virtue of its position relative to the position of another object. Thus it depends on the position of another object with respect to its original position.
Expression for Gravitational potential energy:
Let an object of mass m be lifted or carried upward at a height, h. In doing so we have to do some amount of work to accelerate due to gravity, g. This work done in doing so is stored in the form of energy which is known as gravitational potential energy.

Since we know that,
Work done $=$ Force $\times$ Displacement
Here the force of the object is due to its own weight which is equal to $mg$ and the displacement is equal to height, h.
Therefore we can write as,
$\Rightarrow$ Work done $= {\text{ }}mg{\text{ }} \times {\text{ }}h$
$\Rightarrow$ Work done $= {\text{ }}mgh$
This work done is stored in the form of energy which is known as gravitational potential energy. Since it is the form of energy, therefore its unit will be Joules.

Note:
Since the work is done against the gravitational pull of the earth this is why it is called gravitational potential energy. In potential energy the position change must be relative to other objects. In kinetic energy the energy of an object is due to its motion. While calculating potential energy of a system of two objects one object must be at rest position relative to the other.