Question

The period of a simple pendulum is 3.5 s. The length of the pendulum is doubled. What is the period T of the longer pendulum?

Answer 1

Step-by-step explanation:

The period T of a simple pendulum is given by

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

Doubling the length of the pendulum gives us a new period T'

`T' = 2 \pi \sqrt{(l')/(g)} = 2 \pi \sqrt{(2l)/(g)}`

`\:\:\:\:\:\:\:= √(2) \left(2 \pi \sqrt{(l)/(g)} \right)`

`\:\:\:\:\:\:\:= √(2)\:T = √(2)(3.5\:\text{s})= 4.95\:\text{s}`