Question

What would be the time period of a simple pendulum if its length is increased 4 times?

Answer 1

When the length of a simple pendulum is increased by a factor of 4, the new time period will be twice that of the original period, based on the time period formula T = 2π√(L/g).

Step-by-step explanation:

The time period (T) of a simple pendulum can be found using the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. If the length of the pendulum is increased by a factor of 4, the new time period (T') can be calculated as follows:

1. Start with the original formula T = 2π√(L/g).
2. After increasing the length fourfold, the new length L' = 4 * L.
3. Replace L with 4L in the original formula to get T' = 2π√(4L/g).
4. Simplify to get T' = 2 * 2π√(L/g).
5. Realize that 2π√(L/g) is the original time period T, thus T' = 2T.

Therefore, if the length of the simple pendulum is increased by a factor of 4, the new time period will be twice the original time period of the pendulum.