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 ?

Easy

A

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

$\large \frac {GMmh}{R(R+h)}$
C

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

$\large mgh$

Solution

$\large {\left( {P.E} \right)_A} = - \frac{{GMm}}{R};{\left( {P.E} \right)_B} = - \frac{{GMm}}{{R + h}}$
$\large \therefore \,\Delta U = {\left( {P.E} \right)_B} - {\left( {P.E} \right)_A}$
$\large = - \frac{{GMm}}{{R + h}} + \frac{{GMm}}{R} = \frac{{GMmh}}{{\left( R \right)\left( {R + h} \right)}}$

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