Question

If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius of the earth R, is

• A. $\frac{1}{2}mgR$
• B. 2 mgR
• C. mgR
• D. $\frac{1}{4}mgR$

Answer 1

The correct option is A

$\frac{1}{2}mgR$

Gain in potential energy $△U=\frac{mgh}{1+\frac{h}{R}}$

If h = R then $△U=\frac{mgh}{1+\frac{R}{R}}=\frac{1}{2}mgR$