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7.Gravitation
medium
A spherical planet has a mass $M$ and diameter $D$ . A particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity , equal to
A
$\frac{{4GM}}{{{D^2}}}$
B
$\frac{{GM}}{{{D^2}}}$
C
$\frac{{GMm}}{{{D^2}}}$
D
$\frac{{4GMm}}{{{D^2}}}$
(AIPMT-2012)
Solution
Gravitational force acting on particle of mass $m$ is
$F = \frac{{G{M_p}m}}{{{{\left( {{D_p}/2} \right)}^2}}}$
Acceleration due to gravity experience by the particle is
$g = \frac{F}{m} = \frac{{G{M_p}}}{{{{\left( {{D_p}/2} \right)}^2}}} = \frac{{4G{M_p}}}{{D_p^2}}$
Standard 11
Physics
