If a simple pendulum is mounted in a car that is moving with a constant speed $v$ along a circular t

Question

If a simple pendulum is mounted in a car that is moving with a constant speed $v$ along a circular track of radius $R$, what is its time period of oscillation?

Professor PC Thomas Classes · Answer

The bob experiences both gravity downwards and a centrifugal pseudo-force outward. The effective gravity is the vector sum: $g_{eff} = \sqrt{g^2 + (v^2/R)^2}$. Therefore, $T = 2\pi\sqrt{L/g_{eff}}$.