Question

The original period of a simple pendulum is T. The length of the simple pendulum is then quadrupled and its mass isdoubled. What is the new period of the simple pendulum in terms of T?

Answer 1

The new period of a simple pendulum with quadrupled length and doubled mass is twice the original period T, given that the period is independent of mass.

Step-by-step explanation:

The original period of a simple pendulum is T. If the length of the simple pendulum is then quadrupled and its mass is doubled, the new period will be affected only by the change in length since the period of a pendulum is independent of the mass. Using the formula for the period of a simple pendulum, T = 2π√(L/g), where L is the length and g is the acceleration due to gravity, we find that quadrupling the length of the pendulum will affect the period as follows:

T' = 2π√(4L/g) = 2*2π√(L/g) = 2*T

Therefore, the new period T' is twice the original period T.

Answer 2

Recall that the time period of a simple pendulum is given by

`T=2\pi\sqrt[]{(l)/(g)}`

Where l is the length of the pendulum and g is the acceleration due to gravity.

The mass of the pendulum has no effect upon the time period of the pendulum.

If the length of the simple pendulum is quadrupled (4 times) then the period becomes

`T=2\pi\sqrt[]{(4l)/(g)}`

Let us re-write the above equation in terms of T

`\begin{gathered} T=2\pi\sqrt[]{(4l)/(g)} \\ T=\sqrt[]{4}\cdot(2\pi\sqrt[]{(l)/(g)}) \\ T=2\cdot(T) \\ T=2T \end{gathered}`

Therefore, the new period of the simple pendulum is doubled (2 times) as compared to the original period.

The correct answer is option B