Question

calculate the change in the length of a simple pendulum of length 1m, when it's period of oscillation change from 2sec to 1.5 sec

Answer 1

Hey there!

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 .

$\therefore$ The change in length of pendulum is 0.4375 m .

Hope helped!