Find the work required to raise a mass m from the Earth’s surface to an altitude equal to the Earth’s radius R. Let g denote surface gravitational acceleration.
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Question

Find the work required to raise a mass m from the Earth’s surface to an altitude equal to the Earth’s radius R. Let g denote surface gravitational acceleration.

G1 Physics · Accepted Answer

Step 1: Gravitational potential energy of mass m at distance r from Earth’s centre is U(r) = −GMm/r. Step 2: Initial position r(initial) = R; final position r(final) = 2R. Step 3: Work by an external agent in a quasistatic lift is ΔU = U(2R) − U(R) = −GMm/(2R) + GMm/R = GMm/(2R). Step 4: Since g = GM/R², GM/R = gR. Therefore ΔU = ½mgR. Final answer: mgR/2 (Option A).