Answer :
Answer:
The value of the acceleration of gravity on this planet is [tex]11.4\ m/s^2[/tex].
Explanation:
Given that,
Length of the simple pendulum, l = 55 cm = 0.55 m
The explorer finds that the pendulum completes 93.0 full swing cycles in a time of 129 s. The time period is given by :
[tex]T=\dfrac{129}{93}=1.38\ s[/tex]
We need to find the value of the acceleration of gravity on this planet. The time period in case of simple pendulum is given by :
[tex]T=2\pi \sqrt{\dfrac{l}{g}}\\\\g=\dfrac{4\pi ^2l}{T^2}[/tex]
[tex]g=\dfrac{4\pi ^2\times 0.55}{(1.38)^2}\\\\g=11.4\ m/s^2[/tex]
So, the value of the acceleration of gravity on this planet is [tex]11.4\ m/s^2[/tex]. Hence, this is the required solution.