Question

A simple pendulum of length 2.5 m makes 5.0 complete swings in 16 s. What is the acceleration of gravity at the location?

Answer 1

The acceleration of gravity at the location is 9.64 m/s²

Explanation:

Length of pendulum = 2.5 m

Time taken for 5 swings = 16 seconds

Time taken for 1 swing = 3.2 seconds

Period of pendulum = 3.2 seconds.

We have equation for period of simple pendulum as

             $T=2\pi \sqrt{\frac{l}{g}}$

Where l is the length of pendulum and g is acceleration due to gravity.

Substituting

                 $T=2\pi \sqrt{\frac{l}{g}}\\\\3.2=2\pi \sqrt{\frac{2.5}{g}}\\\\g=\frac{4\pi^2 \times 2.5}{3.2^2}\\\\g=9.64m/s^2$

The acceleration of gravity at the location is 9.64 m/s²