A body of mass is taken from the surface of earth to a height equal to twice the radius of earth . The increase in potential energy will be

Question

A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth $(R_{e})$ . The increase in potential energy will be ______. [2026]

( $g$ is acceleration due to gravity at the surface of earth)

Smart Achievers · Accepted Answer

(4)

$U_{1} = - \frac{G M m}{R_{e}}$

$U_{2} = \frac{- G M m}{R_{e} + 2 R_{e}} = - \frac{G M m}{3 R_{e}}$

$Δ U = U_{2} - U_{1} = - \frac{G M m}{3 R_{e}} + \frac{G M m}{R_{e}}$

$Δ U = \frac{2}{3} \frac{G M m}{R_{e}} = \frac{2}{3} [\frac{G M}{R_{e}^{2}}] (m R_{e})$

$\Rightarrow Δ U = \frac{2}{3} m g R_{e}$

Solution

Q.
A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth $(R_{e})$ . The increase in potential energy will be ______. [2026]

( $g$ is acceleration due to gravity at the surface of earth)

1 $\frac{1}{2} m g R_{e}$

2 $\frac{3}{4} m g R_{e}$

3 $\frac{1}{4} m g R_{e}$

4 $\frac{2}{3} m g R_{e}$

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Solution

Q. A body of mass m is taken from the surface of earth to a height equal to twice the radius of earth (Re). The increase in potential energy will be ______. [2026] (g is acceleration due to gravity at the surface of earth)

1 12mgRe

2 34mgRe

3 14mgRe

4 23mgRe