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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.

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?

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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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