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The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be :

  • Option 1)

    \frac{\sqrt{3}}{2} s

  • Option 2)

    \frac{3}{2} s

  • Option 3)

    \frac{2}{\sqrt{3}} s

  • Option 4)

    2\sqrt{3} s

Answers (1)

best_answer

 

Time period of oscillation of simple pendulum -

T=2\pi \sqrt{\frac{l}{g}}

- wherein

l = length of pendulum 

g = acceleration due to gravity.

 

M_{P}=3M_{e}

D_{P}=3D_{e}

\Rightarrow r_{P}=3r_{e}

T_{e}=2s

T_{P}=?

T\propto \frac{1}{\sqrt{9}}

&  g=\frac{GM}{R^{2}}

\Rightarrow \frac{T_{p}}{T_{e}}=\sqrt{\frac{g_{e}}{g_{p}}}=\sqrt{\frac{M_{e}}{\left ( R_{e} \right )^{2}}\times \frac{\left ( R_{p} \right )^{2}}{M_{p}}}

\frac{T_{p}}{T_{e}}=\sqrt{\left ( \frac{M_{e}}{M_{p}} \right )\times \left ( \frac{r_{p}}{r_{e}} \right )^{2}}

       =\sqrt{\frac{1}{3}\times \left ( 3 \right )^{2}}

\frac{T_{p}}{T_{e}}=\sqrt{3}

T_{p}=\sqrt{3}T_{e}

T_{p}=\sqrt{3}\times 2

T_{p}=2\sqrt{3}s

 

 


Option 1)

\frac{\sqrt{3}}{2} s

Option 2)

\frac{3}{2} s

Option 3)

\frac{2}{\sqrt{3}} s

Option 4)

2\sqrt{3} s

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