Question

two balls of masses 'm' each are raised to height 'h' and '2h' respectively. What will be the ratio of their potential energies?

Answer 1

Potential energy of ball 1= mgh

Potential energy of ball 2= mg2h

Ratio= mgh/mg2h

m, g and h will get cut.

So, ratio =1/2 = 1:2

Answer 2

The ratio of their potential energies will be 1:2

Given : Two balls of masses 'm' each are raised to height 'h' and '2h' respectively.

To find : The ratio of their potential energies.

Solution :

We can simply solve this numerical problem by using the following process. (our goal is to calculate the ratio of their potential energies)

Here, we will be using the following mathematical formula.

Potential energy = mass of the object × acceleration due to gravity × height at which the object is raised

In the case of first ball,

• mass = m
• acceleration due to gravity = Let, g
• height of the object = h

Potential energy of first ball = m × g × h = mgh

In the case of second ball,

• mass = m
• acceleration due to gravity = Let, g (as the place was same, so gravitational acceleration will be same for the two balls)
• height of the object = 2h

Potential energy of first ball = m × g × 2h = 2mgh

Ratio of their potential energies :

= mgh : 2mgh

= 1:2

(This will be considered as the final result.)

Hence, the ratio of their potential energies is 1:2