# Q .14.17 A simple pendulum of length l and having a bob of mass $M$ is suspended in a car.The car is moving on a circular track of radius $R$ with a uniform speed $V$. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?

S Sayak

Acceleration due to gravity = g (in downwards direction)

Centripetal acceleration due to the circular movement of the car = ac

$a_{c}=\frac{v^{2}}{R}$ (in the horizontal direction)

Effective acceleration is

$\\g'=\sqrt{g^{2}+a_{c}^{2}}\\ g'=\sqrt{g^{2}+\frac{v^{4}}{R^{2}}}$

The time period is T'

$\\T'=2\pi \sqrt{\frac{l}{g'}}\\ T'=2\pi \sqrt{\frac{l}{\sqrt{g^{2}+\frac{v^{4}}{R^{2}}}}}$

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