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7.Gravitation
normal
The mass and diameter of a planet are twice those of earth. What will be the period of oscillation of a pendulum on this planet if it is a seconds pendulum on earth ?
A
$\sqrt{2}$ second
B
$2 \sqrt{2}$ seconds
C
$\frac{1}{\sqrt{2}}$ second
D
$\frac{1}{2\sqrt{2}}$ second
Solution
$g=\frac{G M}{R^{2}}$ and $g^{\prime}=\frac{G \cdot 2 M}{4 R^{2}}$
$=\frac{1}{2} g$
$T \propto \frac{1}{\sqrt{g}} \Rightarrow \frac{T_{2}}{T_{1}}=\sqrt{\frac{g_{1}}{g_{2}}}$
$T=\sqrt{\frac{g}{g / 2}}=\sqrt{2}$
$\therefore T_{2}=\sqrt{2} T_{1}=2 \sqrt{2} \mathrm{s}$
Standard 11
Physics
