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Question:

The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is :

12mgR

mgR

32mgR

2 mgR

Solution:

Correct option is C. 1/2mgR
Initial potential energy at earth's surface is
Ui = −GMm/R
Final potential energy at height h = R
Uf = −GMm/2R
As work done = change in PE
∴W = Uf − Ui = GMm/2R (∵GM = gR²)= gR²m/2R = mgR/2