# Diameter And Mass Of A Planet Are Double That Earth. Then Time Period Of A Pendulum At Surface Of Planet Is How Much Times Of Time Period At Earth Surface

Time period of simple pendulum, $t = 2\pi \sqrt{\frac{L}{g}}$

For earth, g = $\frac{GM_{E}}{R}$

For planet, $M_{P} = 2M_{E} R_{P} = 2R$ $g_{P} = \frac{G(2M_{E})}{(2R)^{2}}$ $\Rightarrow g_{P} = \frac{g}{2}$

Now, $\frac{t_{p}}{t_{E}} = \sqrt{\frac{g}{g/2}}$ $\Rightarrow t_{P} = \sqrt{2}t_{E}$

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