Answer: 4g
Explanation:
Given
The time on earth is 4 s for 20 oscillations
i.e. time period for one oscillation is [tex]\frac{4}{20}=\frac{1}{5}\ s=0.2\ s[/tex]
for planet X it is 40 oscillations in 4 s i.e.
time period is [tex]\frac{4}{40}=0.1\ s[/tex]
The time period of a pendulum is given by
[tex]T=2\pi\sqrt{\dfrac{L}{g}}[/tex]
where L=length of the pendulum
g=acceleration due to gravity
So, we can write the ratio of the time period of two pendulums as
[tex]\frac{0.2}{0.1}=\dfrac{2\pi\sqrt{\frac{L}{g}}}{2\pi\sqrt{\frac{L}{g'}} }[/tex]
[tex]2=\sqrt{\frac{g'}{g}}[/tex]
[tex]\sqrt{g'}=2\sqrt{g}\\g'=4g[/tex]
i.e. 4 times the gravity of the earth
