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  • An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy?

An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy?

Answers (1)

Let PE_{i}  be the initial P.E when mass is at the surface of earth

Let PE_{f} be the final P.E when mass is lifted to height equal to R

PE_{i}=-\frac{GMm}{R}

PE_{f}=-\frac{GMm}{2R}

Gain in PE=PE_{f}-PE_{i}=-\frac{GMm}{2R}-\left (-\frac{GMm}{R} \right )=\frac{GMm}{2R}

GM=gR^{2}

Gain in PE=\frac{1}{2}mg\; R

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