Question

How is the time period of a simple pendulum affected, if at all, in the following situations:

1. The length is made four times.
2. The acceleration due to gravity is reduced to one-fourth.

Answer 1

We know that, `"T" = 2pisqrt(l/"g")`

(a) If length quadruples then,

`T'  = 2pisqrt((4l)/"g")`

or, `T/(T')`

= `(2pisqrt(l/"g"))/(2pisqrt((4l)/"g"))`

= `1/2` 

or, T = 2T'

Therefore, the time period is doubled.

(b) If the acceleration due to gravity is reduced to one-fourth,

`T'  = 2pisqrt(l/(1/4"g"))`

or, `"T"/("T"')`

= `(2pisqrt(l/"g"))/(2pisqrt(l/(1/4"g"))`

= `1/2`

or, T = 2T'

Therefore, the time period is doubled.