Answer:
g = 11.2 m/s²
Explanation:
First, we will calculate the time period of the pendulum:
[tex]T = \frac{t}{n}[/tex]
where,
T = Time period = ?
t = time taken = 135 s
n = no. of swings in given time = 98
Therefore,
[tex]T = \frac{135\ s}{98}[/tex]
T = 1.38 s
Now, we utilize the second formula for the time period of the simple pendulum, given as follows:
[tex]T = 2\pi \sqrt{\frac{l}{g}}[/tex]
where,
l = length of pendulum = 54 cm = 0.54 m
g = acceleration due to gravity on the planet = ?
Therefore,
[tex](1.38\ s)^2 = 4\pi^2(\frac{0.54\ m}{g} )\\\\g = \frac{4\pi^2(0.54\ m)}{(1.38\ s)^2}[/tex]
g = 11.2 m/s²
