Question

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

Answer 1

Answer: (B)

$g=\frac{G M}{R^{2}} $ &$ g^{\prime}=\frac{G(2 M)}{(2 R)^{2}} $
so $g^{\prime}=\frac{g}{2}$
$T^{\prime}=2 \pi \sqrt{\frac{2 \ell}{g}} $
$ \Rightarrow T^{\prime}=\sqrt{2} T $
$\Rightarrow T^{\prime}=2 \sqrt{2}$sec.