Question

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

Answer 1

The relation is T α √(l/g)

Hence if lenght is four times, time period is 2 times..
and if g is 1/4 times time period is 2 times

Answer 2

T =2π√l/g    ie T the period is directly proportional to the squre root of  l the length of the string and inverselyproportional to g the accelaration due to gravity.here when length is doubled,period will be increased by 2 times. when the accelaration due to gravity is reduced by 1/4th ,then period is inncreased by 2 times