The height above the Earth surface of two bodies having similar masses is in the ratio 2:1. The ratio of their potential energy will be ______?

Concept Used:

Gravitational potential energy (U) of a body at a height above the Earth's surface is given by:

U = m × g × h

m: Mass of the body

g: Acceleration due to gravity

h: Height above the Earth's surface

Calculation:

Let the heights be h₁ and h₂.

Given: h₁ : h₂ = 2 : 1

From the formula for potential energy:

U₁ = m × g × h₁

U₂ = m × g × h₂

Taking the ratio of potential energies:

U₁ / U₂ = (m × g × h₁) / (m × g × h₂)

⇒ U₁ / U₂ = h₁ / h₂

⇒ U₁ / U₂ = 2 / 1

⇒ U₁ : U₂ = 2 : 1

∴ The ratio of their potential energy is 2:1.