A body of mass 'm' is raised to a height ′10R′ from the surface of earh, where 'R' is the radius of earth. The increase in potential energy is (G= universal constant of gravitation, M=mass of earth and g= acceleration due to gravity).
GMm11R
mgR11G
GMm10R
10GMm11R
A
GMm10R
B
10GMm11R
C
mgR11G
D
GMm11R
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Solution
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Potential energy at point U=−GMmr
where r is the distance of the point from the earth surface.
Thus potential energy at earth surface i.e. r=R, U1=−GMmR
Potential energy at a height 10R above earth surface i.e. r=11R, U2=−GMm11R
Increase in potential energy ΔU=U2−U1
Or ΔU=−GMm11R−(−GMmR)
Or ΔU=GMmR[−111+1]
⟹ΔU=10GMm11R
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