First slide

Gravitaional potential energy

Question

Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final – initial) of an object of mass m, when taken to a height h from the surface of earth (of radius R), is given by,

Moderate

A

$\frac{GMm}{R + h}$
B

$- \frac{GMm}{R + h}$
C

$\frac{GMmh}{R (R + h)}$
D

mgh

Solution

$(P . E)_{A} = - \frac{GMm}{R}$
$(P . E)_{B} = - \frac{GMm}{R + h}$
$∴ ΔU = (P . E)_{B} - (P . E)_{A}$
$= - \frac{GMm}{R + h} + \frac{GMm}{R} = \frac{GMmh}{(R) (R + h)}$

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