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

Step-by-step solution

The potential energy of an object at the surface of the earth U₁=- G M m R The potential energy of the object at a height h=R from the surface of the earth U₂=- G M m R+h =- G M m R+R Hence, the gain in potential energy of the object aligned U &=U₂-U₁ U &=- G M m R+R + G M m R U &=- G M m 2 R + G M m R U &= 1 2 G M m R aligned But we know that G M=g R² Hence, U= 1 2 g R² m R or U= 1 2 g R m or U= 1 2 m g R