# If g is the acceleration due to gravity of the earth’s surface the gain in 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 Option 1) $\frac{1}{2} mgR$ Option 2) $2 mgR$ Option 3) $mgR$ Option 4) $\frac{1}{4} mgR$

As we learnt in

Gravitational Potential energy at a point -

$W=-\frac{GMm}{r}$

$U=-\frac{GMm}{r}$

$U\rightarrow$ gravitational potential energy

$M\rightarrow$ Mass of source body

$m\rightarrow$ mass of test body

$r\rightarrow$ distance between two

- wherein

Always negative in the gravitational field because Force is attractive in nature.

Potential energy at earth's surface $=-\frac{GMm}{R}=-mgr$

Potential energy at height $R=-\frac{mgR}{2}$

$\therefore$ gain in potential energy $=-\frac{mgR}{2}+mgR=\frac{mgR}{2}$

Option 1)

$\frac{1}{2} mgR$

This is correct option

Option 2)

$2 mgR$

This is incorrect option

Option 3)

$mgR$

This is incorrect option

Option 4)

$\frac{1}{4} mgR$

This is incorrect option

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