Question

The mass and diameter of a planet are twice those of earth. The period of oscillation of a pendulum on this planet if it is a seconds pendulum on earth is:

• A. 2$\sqrt{3}$s
• B. 2$\sqrt{2}$s
• C. 2s
• D. 4s

Answer 1

The correct option is B 2$\sqrt{2}$s

$T=2\pi \sqrt{\frac{l}{g}}$
$T_1=2\pi \sqrt{\frac{l{R}^2}{Gm}}$
$T_2=2\pi \sqrt{\frac{l(2R{)}^2}{G\times \left(2m\right)}}$
$\frac{T_1}{T_2}=\frac{1}{\sqrt{2}}$
$T_2=T_1\sqrt{2}$
$\therefore T_2=2\sqrt{2}sec$