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, [latex]t = 2\pi \sqrt{\frac{L}{g}} [/latex]

For earth, g = [latex]\frac{GM_{E}}{R} [/latex]

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

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

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