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) The acceleration due to gravity is reduced to one-fourth.

As we know that,

T = 2π \sqrt {l\over g }

where,

• T = Time period
• l = effective length of the pendulum
• g = acceleration due to gravity.

(a) In the case when length is made four times, let time period be T₁, we see that

T₁ = 2π \sqrt {4l\over g }

T₁ = 2π \sqrt {l\over g }

T₁ = 2 × T

Hence, we can say that when the length is made four times, time period of a simple pendulum is doubled.

(b) In the case, when acceleration due to gravity is reduced to one fourth, let time period be T₁, we see that —

T₁ = 2π \sqrt {l\over g/4 }

T₁ = 2π \sqrt {4l\over g }

T₁ = 2π \sqrt {l\over g }

T₁ = 2 × T

Hence, we can say that when acceleration due to gravity is reduced to one fourth, time period of a simple pendulum is doubled.