Question

A visitor to a lighthouse wishes to determine the height of the tower. She ties a spool of thread to a small rock to make a simple pendulum, which she hangs down the center of a spiral staircase of the tower. The period of oscillation is 6.40 s. What is the height of the tower

Answer 1

l = 10.16 m

Step-by-step explanation:

In this case, we have the period of oscillation of the pendulum is 6.4 s. It is required to find the height of the tower.

We know that the pendulum executes SHM. Let l is the height of the tower. The time period of simple pendulum is given by :

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

g is acceleration due to gravity

We need to rearrange the above equation such that,

`l=(T^2g)/(4\pi ^2)\\\\l=((6.4)^2* 9.8)/(4\pi ^2)\\\\l=10.16\ m`

So, the height of the tower is 10.16 m.