Question

By what factor should the length of a simple pendulum be changed in order to triple the period of vibration?

Answer 1

9 times of the previous length

Explanation:

Relation between time period T and length l of pendulum is given as T `prop` √l
So, we can write,
`(T2)/(T1)` = `√(l2)/(l1)` (where T1 and T2 are initial and final time period and L1 and L2 are initial and final length of the pendulum respectively as required)
Given, T2 = 3 T1
So, `(l2)/(l1)` will be 9
Hence length should be made 9 times than that of the previous value.