Question

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 54.0 cm. The explorer finds that the pendulum completes 98.0 full swing cycles in a time of 135s.

Required:
What is the value of g on this planet?

Answer 1

g = 11.2 m/s²

Step-by-step explanation:

First, we will calculate the time period of the pendulum:

`T = (t)/(n)`

where,

T = Time period = ?

t = time taken = 135 s

n = no. of swings in given time = 98

Therefore,

`T = (135\ s)/(98)`

T = 1.38 s

Now, we utilize the second formula for the time period of the simple pendulum, given as follows:

`T = 2\pi \sqrt{(l)/(g)}`

where,

l = length of pendulum = 54 cm = 0.54 m

g = acceleration due to gravity on the planet = ?

Therefore,

`(1.38\ s)^2 = 4\pi^2((0.54\ m)/(g) )\\\\g = (4\pi^2(0.54\ m))/((1.38\ s)^2)`

g = 11.2 m/s²