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7.Gravitation
hard
The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is $2\,s$. The period of oscillation of the same pendulum on the planet would be
A
$\frac{{\sqrt 3 }}{2}\,s$
B
$\frac{2}{{\sqrt 3 }}\,s$
C
$\frac{3}{2}\,s$
D
$2\sqrt 3 \,s$
(JEE MAIN-2019)
Solution
$g = \frac{{GM}}{{{R^2}}}$
$\frac{{{g_p}}}{{{g_e}}} = \frac{{{M_p}}}{{{M_e}}}{\left( {\frac{{{R_e}}}{{{R_p}}}} \right)^2} = 3{\left( {\frac{1}{3}} \right)^2} = \frac{1}{3}$
$Also,\,T \propto \frac{1}{{\sqrt g }}$
$ \Rightarrow \frac{{{T_p}}}{{{T_e}}} = \sqrt {\frac{{{g_e}}}{{{g_p}}}} = \sqrt 3 $
$ \Rightarrow {T_p} = 2\sqrt {3s} $
Standard 11
Physics
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