The new period of the pendulum when it is taken to the new planet is double of its period on Earth.
The period of a pendulum is given by the following formula;
[tex]T = 2\pi \sqrt{\frac{l}{g} }[/tex]
where;
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]
[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
