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  4. The time period of oscillations of a second's pendulum on the surface of a planet having mass and radius double. those of earth is

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Q. The time period of oscillations of a second's pendulum on the surface of a planet having mass and radius double. those of earth is

Oscillations

Solution:

$g_{1}=\frac{G m}{R^{2}}$
$g_{2}=\frac{G \times 2 m}{4 R^{2}}=\frac{g_{1}}{2} $
$T_{1}=2 \pi \sqrt{\frac{l}{g_{1}}}$
$T_{2}=2 \pi \sqrt{\frac{l}{g_{2}}} $
$T_{2}=\sqrt{2} T_{1}$
Since $T_{1}$ is time period of seconds pendulum $T_{1}=2$.
Hence $T_{2}=2 \sqrt{2}$