Question

Calculate the change in length of a simple pendulum of a length 1m.when period of oscillation changes from 2 sec to 1.5sec

Answer 1

Given Initial time period = 2sec

New time period = 1.5sec

Actual length of pendulum = 1m .

Let the new length be x.

We know that ,

Time period of a simple pendulum is directly proportional to square root of length of pendulum.

" T ∝ √L " or T² ∝ L.

Now,

T1²/T2² = L1 /L2

Substituting the values :

(2²)/(1.5)² = 1/x

4/2.25 = 1/x

=> x = 2.25 / 4

=> x = 0.5625m.

Change in length of Simple pendulum = 1 - 0.5625 = 0.4375 .

The change in length of pendulum is 0.4375 m .