By what factor should the length of a simple pendulum be changed in order to triple the period of vibration?
a. 3
c. 9
b. 6
d. 27

The length of the simple pendulum increased by a factor of 9.

Explanation:

The time period of vibration of a simple pendulum is given by :

.........(1)

l is the length of the simple pendulum

g is the acceleration due to gravity

If the time period of the simple pendulum is tripled, T' = 3 T

The new time period is given by :

..........(2)

Dividing equation (1) and (2) we get :

So, the length of the simple pendulum increased by a factor of 9. Hence, the correct option is (c) "9".

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increases it