Question

The diagram shows a small weight is swinging backwards and forwards on the end of a string. The time for one swing is proportional to the square root of the length of the string. If the length is 64 cm, the time of one swing is 1.6 s. Work out the time of one swing if the length is 144 cm.

Answer 1

2.4 seconds

Explanation:

It is given that,

The time for one swing is proportional to the square root of the length of the string.

`T\propto √(L)`

or

`(T_1)/(T_2)=\sqrt{(L_1)/(L_2)}` ....(1)

We have,

L₁ = 64 cm, T₁ = 1.6 s, L₂ = 144 cm, T₂ = ?

Substitute all the values in formula (1).

`T_2=\frac{T_1}{\sqrt{(L_1)/(L_2)}}\\\\T_2=\frac{1.6}{\sqrt{(64)/(144)}}\\\\T_2=2.4\ s`

So, the new time period of the simple pendulum is 2.4 seconds.