The length of a simple pendulum is made one-fourth. Its time period becomes :
(a) four times (b) one-fourth
(c) double (d) half.
The time period of the simple pendulum is given as
T=2π√lg where, l = length of the pendulum.----------(1)
Now according to the question when the length becomes one-fourth
The time period is written as
From equations 1 and 2 we can say that the new time period is half of its original value.
Hence, The time period of a simple pendulum is proportional to the square root of its length, so if the length is made one-fourth; the time period of the pendulum will become half.
Hence, option (d) is correct.