## Gravitational Potential Energy – Class 11 | Chapter – 8 | Physics Short Notes Series PDF for NEET & JEE

Gravitational Potential Energy: It is the energy an object possesses due to its position in a gravitational field. It is defined as the work done against gravity in moving an object from a reference point to its current position. The gravitational potential energy of an object increases as it is lifted to a higher position in a gravitational field, and decreases as it is lowered to a lower position. The higher an object is above the reference point, the more gravitational potential energy it has.

## Formula of Gravitational Potential Energy

The formula for gravitational potential (PE) Energy is:

PE = mgh

Where,

• m is the mass in kilograms
• g is the acceleration due to gravity (9.8 on Earth)
• h is the height above the ground in meters

## Expression for Gravitational Potential Energy at Height (h)

If a body is taken from the surface of the earth to a point at a height ‘h’ above the surface of the earth, then r= R and r= R + h then,

ΔU = GMm [1/R – 1/(R+h)]

ΔU = GMmh/R(R + h)

When, h<<R, then, R + h = R and g = GM/R2.

On substituting this in the above equation we get,

Gravitational Potential Energy ΔU = mgh

⇒ Note:

• The weight of a body at the centre of the earth is zero due to the fact that the value of g at the centre of the earth is zero.
• At a point in the gravitational field where the GPE is zero, the gravitational field is zero.

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