Question

The length of a simple pendulum is made one-fourth. Its time period becomes :

(a) four times (b) one-fourth

(c) double (d) half.

Answer 1

We know,

The time period of the simple pendulum is given as

$T=2\pi \sqrt{\frac{l}{g}}$ where, l = length of the pendulum.----------(1)

Now according to the question when the length becomes one-fourth

The time period is written as

$T^{\prime }=2\pi \sqrt{\frac{\frac{l}{4}}{g}}=2\pi \times \frac{1}{2}\sqrt{\frac{l}{g}}$ ----------(2)

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.