If the acceleration due to gravity at the surface of theearth is g, the work done in slowly lifting a body of mass m from the earth's
If the acceleration due to gravity at the surface of theearth is g, the work done in slowly lifting a body of mass m from the earth's surface to a height R equal to the radius of the earth is.
(a) 1/2 mgR
(b) 2mgR
(c) mgR
(d) 1/4 mgR.
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The correct answer is (a) 1/2 mgR
EXPLANATION:
The distance of the body from the center of the earth at a height R from the earth's surface = 2R. The acceleration due to gravity at distance x from the center of the earth ( for x>R) = GM/x²
Force on the body by the earth =mGM/x²
Since the body is lifted slowly, hence the moving force is ≈ mGM/x²
Hence the work done by the force in taking the body from R to 2R
= ∫m(GM/x²)dx
(limit of integration from R to 2R)
=mGM[-1/x]
=mGM[-1/2R+1/R]
=mGM/2R
=½m(GM/R²)R
= ½mgR
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