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Time period of a simple pendulum on the surface of a planet of radius R is T and the escape velocity on the surface of this planet is v . Time period of oscillation of the same pendulum on the surface of another planet of radius 4R is 2T. What will be the escape velocity on the surface of this new planet?

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Detailed Solution

V=2GMR=2gR;T=2πlg⇒g=4π2lT2∴V=2.4π2lT2.R=2π2l.RT⇒V∝RT∴V'V=4RR.T2T=1⇒V'=V

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Time period of a simple pendulum on the surface of a planet of radius R is T and the escape velocity on the surface of this planet is v . Time period of oscillation of the same pendulum on the surface of another planet of radius 4R is 2T. What will be the escape velocity on the surface of this new planet?