Question

The mass and diameter of a planet are twice those of earth. The period of oscillation of pendulum on this planet will be (If it is a second's pendulum on earth)

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

As we know $g=\frac{GM}{R^2}$
$\Rightarrow \frac{g_{earth}}{g_{plant}}=\frac{M_e}{M_p}\times \frac{R_p^2}{R_e^2}\Rightarrow \frac{g_e}{g_p}=\frac{2}{1}$
Also $T\propto \frac{1}{\sqrt{g}}\Rightarrow \frac{T_e}{T_p}=\sqrt{\frac{g_p}{g_e}}\Rightarrow \frac{2}{T_p}=\sqrt{\frac{1}{2}}$
$\Rightarrow T_p=2\sqrt{2}sec.$