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What is the new period if the pendulum is taken to a planet that has 4 times the mass and 4 times the radius of earth

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onyebuchinnaji

The new period of the pendulum when it is taken to the new planet is  double of its period on Earth.

Period of a pendulum

The period of a pendulum is given by the following formula;

[tex]T = 2\pi \sqrt{\frac{l}{g} }[/tex]

where;

  • g is acceleration due to gravity of the pendulum
  • L is length of the pendulum

Acceleration due to gravity of the new planet

The acceleration due to gravity of the new planet is calculated as follows;

[tex]g_E = \frac{GM_E}{R_E^2} = 9.81 \ m/s^2 \\\\g(new \ planet) = \frac{G(4M_E)}{(4R_E)^2} = \frac{4GM_E}{16R_E^2} = \frac{GM_E}{4R_E^2} = \frac{9.81}{4} = 2.45 \ m/s^2[/tex]

New period of the pendulum

[tex]T = 2\pi \sqrt{\frac{l}{g} } \\\\T =\frac{2\pi \sqrt{l} }{\sqrt{g} } \\\\T_1\sqrt{g_1} = T_2\sqrt{g_2} \\\\T_E\sqrt{g_E} = T\sqrt{g} \\\\T = \frac{T_E\sqrt{g_E}}{\sqrt{g} } \\\\T = \frac{T_E \times \sqrt{9.81} }{\sqrt{2.45} } \\\\T = 2T_E[/tex]

Thus, the new period of the pendulum when it is taken to the new planet is double of its period on Earth.

Learn more about period of pendulum here: https://brainly.com/question/26449711

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