Question

A body of mass m is taken from Earth's surface to the height equal to half of radius of Earth . The increase in potential energy will be ?​

1. mgR
2. 1/3 mgR
3. 3mgR
4. 1/4 mgR
​

Answer 1

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Answer 2

Given:

Mass of the body = m

Height at which the body is raised = R

To find:

The increase in the potential energy.

Solution:

If we consider the potential energy at the surface of Earth as 0.

The value of acceleration due to gravity decreases g' = gR/ (R+R/2) = 2g/3

Then potential energy at a height equal to R/2 will be m*2g/3*(R/2) = mgR/3

Increase in potential energy = Final - Initial

= mgR/3-0 = mgR/3

The increase in potential energy will be 1/3 mgR.