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If g is the acceleration due to gravity ...

If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is

A

`1/2 mgR`

B

`2mgR`

C

`mgR`

D

`1/4 mgR`

Text Solution

Verified by Experts

The correct Answer is:
A
Potential energy at the surface of the earth
` =- (GMm)/( R) = - (GM)/(R^2) m R = - g mR " " ( because g = (GM)/(R^2))`
Potential energy at a distance R from the surface of the earth
` = - (GMm)/((R + R))= - (GMm)/(2R) = - (gmR)/(2)`
` therefore ` Gain in the potential energy = `- (gmR)/(2) - (-gmR) = 1/2 mgR`
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