A simple pendulum of length l is suspended inside a vehicle accelerating horizontally with constant acceleration a. After the bob reaches its new equilibrium direction, it is displaced through a small angle about that direction and released. What is the time period of small oscillations?
Options

Question

A simple pendulum of length l is suspended inside a vehicle accelerating horizontally with constant acceleration a. After the bob reaches its new equilibrium direction, it is displaced through a small angle about that direction and released. What is the time period of small oscillations?

Options

G1 Physics · Accepted Answer

In the accelerating frame, the bob experiences gravity and a horizontal pseudo-acceleration. The magnitude of effective gravity is gₑ = √(g²+a²). Small oscillations occur about the direction of this effective gravity. Therefore, T = 2π√[l/gₑ] = 2π√[l/√(g²+a²)]. Correct option: B.