Question

how will time period of simple pendulum change if(i)its length is made 4 times (ii)the amplitude is doubled?

Answer 1

Dear Student ,
Here in this case let me tell yu at first that the time period of a simple pendulum does not depend on the amplitude so if the amplitude changes the time period remains same .
Now for the first question when the length is made 4 times the original length then , L' = 4L
$$\begin{gathered} Therefore,Timeperiodofsimplependulumis,T=2\pi \sqrt{\frac{L}{g}} \\ So,T\propto \sqrt{L} \\ \Rightarrow \frac{T}{T\text{'}}=\sqrt{\frac{L}{L\text{'}}} \\ \Rightarrow \frac{T}{T\text{'}}=\sqrt{\frac{L}{4L}} \\ \Rightarrow \frac{T}{T\text{'}}=\sqrt{\frac{1}{4}}=\frac{1}{2} \\ \Rightarrow T\text{'}=2T \end{gathered}$$
So the time period becomes 2 times the initial time period .
Regards