If acceleration due to gravity at the surface of the earth 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 :
Answer & explanation
Correct answer: option 1
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