Question

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

Answer 1

$T=2\pi \sqrt{\frac{t}{g}}$
(a) The length is made four times - 'T' is directly proportional to the square root of the

'I' - length of the string and inversely proportional to the acceleration

due to gravity.

Hence the length is doubled when the period is increased by two times.

(b) The acceleration due to gravity is reduced to one - fourth

- when g - acceleration due to gravity,

is reduced by $1/4^{th}$,

the period is increased by 2 times.