Question

A simple pendulum with a period of 2.0s has its length doubled. Its new length will be?

Answer 1

`2.0m`

Step-by-step explanation

First, we have to find the initial length of the pendulum by applying the formula for the period:

`T=2\pi\sqrt[]{(L)/(g)}`

where L = length of the pendulum

g = acceleration due to gravity

Hence, we have that the initial length of the pendulum is:

`\begin{gathered} 2=2\pi\cdot\sqrt[]{(L)/(10)} \\ (2)/(2\pi)=\sqrt[]{(L)/(10)} \\ ((2)/(2\pi))^2=(L)/(10) \\ \Rightarrow L=10\cdot((2)/(2\pi))^2 \\ L=1.0m \end{gathered}`

Hence, the new length of the pendulum after it is doubled is:

`\begin{gathered} L=2\cdot1.0 \\ L=2.0m \end{gathered}`

That is the answer.