Question

Two simple pendula of length L and 4L are pulled aside to the right and are at rest so that they make an angle 30° with the vertical. They are then released simultaneously at time t = 0. The time after which they will be in phase is ______.

Options

• `pi/2 sqrt("L"/"g")`

• `pi sqrt("L"/"g")`

• `2pi sqrt("L"/"g")`

• `4pi sqrt("L"/"g")`

Answer 1

Two simple pendula of length L and 4L are pulled aside to the right and are at rest so that they make an angle 30° with the vertical. They are then released simultaneously at time t = 0. The time after which they will be in phase is `underline(4pi sqrt("L"/"g"))`.

Explanation:

`"T"_1 = 2pi(sqrt("l"/"g")), "T"_2 = 2pisqrt((4"l")/"g") = 4pi sqrt("l"/"g")`

T2 = 2T1, clearly after T2 both will be at origin and also in phase.