Question

if g is the acceleration due to gravity on the earth's surface , the gain in the potential energy of an object is mass m raised from the surface to a height equal to the radius R of the earth , is [AIEEE 2004] ​

Answer 1

Explanation:

Let M, R be the mass and radius of the earth. Then

g=GM/R

2

or GM=gR

2

(i)

Potential energy of the object on the surface of earth

U

1

=

R

−GMm

The potential energy of the object at a height equal to radius of the earth is

U

2

=

2R

−GMm

Gain in PE is

U

2

−U

1

=−

2R

GMm

+

R

GMm

=

2R

GMm

=

2R

(gR

2

)m

=

2

1

mgR.

Answer 2

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