Question

If the period of the pendulum is tripled, what is the length of the string increased by?

Answer 1

Tripling the period of a pendulum does not result in a specific increase in the length of the string.

Step-by-step explanation:

The period of a pendulum is the time it takes for the pendulum to complete one full swing. The period of a pendulum is given by the equation:

T = 2π√(L/g)

Where T is the period, L is the length of the string, and g is the acceleration due to gravity. If we triple the period, we need to find the change in length of the string. Let's assume the original period is T and the original length is L. After tripling the period, the new period becomes 3T. Plugging this into the equation, we get:

3T = 2π√(L/g)

Dividing both sides by 3, we get:

T = (2/3)π√(L/g)

Now, we can compare the original equation with the new equation:

2π√(L/g) = (2/3)π√(L/g)

Canceling out the π and √(L/g) terms, we get:

2 = 2/3

This is not true, so there is no value of L that satisfies the condition of tripling the period. Therefore, the length of the string cannot be increased by a specific amount when the period is tripled.

Answer 2

The period of the pendulum doesn't determine the length of the string.
It's the other way around.

The period of the pendulum is proportional to the square root of its length.
So if you want to triple the period, you have to make the string nine times
as long as it is now.