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Question
How is the time period of a simple pendulum affected, if at all, in the following situations:
- The length is made four times.
- The acceleration due to gravity is reduced to one-fourth.
Solution
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.
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