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

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

$T=2\pi\sqrt[]{\frac{l}{g}}$

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

$T=2\pi\sqrt[]{\frac{4l}{g}}$

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

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

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

The correct answer is option B