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7.Gravitation
medium
A body of mass $m$ kg. starts falling from a point $2R$ above the Earth’s surface. Its kinetic energy when it has fallen to a point $‘R’$ above the Earth’s surface [$R-$Radius of Earth, $M-$Mass of Earth, $G-$Gravitational Constant]
A
$\frac{1}{2}\frac{{GMm}}{R}$
B
$\frac{1}{6}\frac{{GMm}}{R}$
C
$\frac{2}{3}\frac{{GMm}}{R}$
D
$\frac{1}{3}\frac{{GMm}}{R}$
Solution
(b) Potential energy $U = \frac{{ – GMm}}{r} = – \frac{{GMm}}{{R + h}}$
${U_{initial}} = – \frac{{GMm}}{{3R}}$ and ${U_{final}} = – \frac{{ – GMm}}{{2R}}$
Loss in $PE$ = gain in $KE = \frac{{GMm}}{{2R}} – \frac{{GMm}}{{3R}} = \frac{{GMm}}{{6R}}$
Standard 11
Physics
