Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

When the length of a simple pendulum is increased by 36cm, its time period of oscillation is found to increase by 25%. The initial length of the simple pendulum (Acceleration due to gravity is 9.8ms2):
A36cmB25cmC64cmD46cm

Answer
VerifiedVerified
507.9k+ views
like imagedislike image
Hint: Time period of a simple pendulum is defined as the time taken by a pendulum to complete one full oscillation and Amplitude of pendulum is the distance travelled by pendulum from equilibrium position to one extreme side.

Complete step by step answer:
A pendulum is a weight, a massive bob, suspended from a pivot so that it can swing freely under the force of gravity. The length of an ideal simple pendulum is the distance from the pivot point to the center of mass of the bob. The radius of oscillation of a physical pendulum is related to the length of the pendulum, the mass of the pendulum, and the moment of inertia of the pendulum about the pivot point. Time period of a simple pendulum is defined as the time taken by a pendulum to complete one full oscillation
Time period of oscillation of a simple pendulum is given by the formula T=2Πlg
Where,
l is the length of string of pendulum
g is the acceleration due to gravity
Now,
We are given that, when the length of a simple pendulum is increased by 36cm, its time period of oscillation is found to increase by 25%. We have to calculate the initial length of the simple pendulum.
Let the initial time period of simple pendulum,
T=2πlg
Now,
New length of the pendulum,
l=l+36100
New time period of the pendulum,
T=T+25100T=1.25T
Therefore,
T=2πlg
Or,
1.25T=2πl+0.36g
Put, T=2πlg
1.25×2πlg=2πl+0.36g1.25lg=l+0.36g
Squaring both sides,
1.5625×lg=l+0.36g1.5625l=l+0.36l(1.56251)=0.360.5625l=0.36l=0.360.5625=0.64l=0.64m=64cm
The initial length of the simple pendulum is 64cm

So, the correct answer is “Option C”.

Note: Always remember that the time period of oscillation of a simple pendulum does not depend upon the mass of the oscillating object and the amplitude of the oscillation. It only depends upon the length of the pendulum and the acceleration due to gravity.