If the length of a simple pendulum is halved then its period of oscillation is

If the length of a simple pendulum is halved then its period of oscillation is

(1) doubled

(2) halved

(3) increased by a factor of 2

(4) decreased by a factor of 2

Answer: (4) The time period ‘T’ of a simple pendulum is given by T = 2πsqrt(l/g), where l is the length and g is the acceleration due to gravity. Let us suppose g be to be a constant, then T = 2πsqrt(l). So the time period of a pendulum is directly proportional to the square root of its length. So, if the length increases, its time period also increases. It means that it takes longer to complete one oscillation. So when its length is halved, its time period is decreased by a factor of 2.