1. mgR 2. 2mgR 3. 1/2mgR 4. 3/2mgR

Answer: 3. 1/2mgR Work done = change in gravitational potential energy. W=-GMm/R+h+GMm/R . With h=R : W=GMm(1/R-dfrac12R)=GMm/2R . Using GM=gR² : W=1/2mgR .

Topic: Gravitational potential energy and gravitational potential· Gravitation

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 :

1. \(mgR\)

2. \(2mgR\)

3. \(\frac{1}{2}mgR\)

4. \(\frac{3}{2}mgR\)

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Answer: 3. \(\frac{1}{2}mgR\)

Work done \(=\) change in gravitational potential energy.

\(W=-\dfrac{GMm}{R+h}+\dfrac{GMm}{R}\). With \(h=R\): \(W=GMm\left(\dfrac1R-\dfrac1{2R}\right)=\dfrac{GMm}{2R}\).

Using \(GM=gR^2\): \(W=\dfrac12mgR\).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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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 :

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