Question

What will be the time period of a simple pendulum if the length of the pendulum is made 9 times the original length.

Answer 1

Answer:

The formula for the period of a simple pendulum is T=2*pi*(Length of pendulum/accelertion due to gravity)^(1/2)

For a simple pendulum of length L, the period is given by T1=2*pi*(L/g)^(1/2)

For a simple pendulum of length 9L, the period is given by T2=2*pi*(9L/g)^(1/2)=6*pi*(L/g)^(1/2)

Comparing these two, we see that T2=3*T1

So multiplying the length by nine will cause the period to triple, or increase by 300%

Hope that helps you!!!

Answer 2

This formula shows the 100% of the length L. Multiplying T and L by 9 and squaring both sides we get 9 * T^2 = 4 * pi^2 * 9 * L/g . Taking the square root of both sides we have 3 * T = 2 * pi * (square root of 9 * L/g). The new formula shows that the former period T becomes 300% of its original value.