physics ncert solutions class 11th Physics Class 11th Oscillations

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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Answered by

Vishal Baghel | Contributor-Level 10

5 months ago

The bob of the simple pendulum will experience the acceleration due to gravity and the centripetal acceleration provided by the circular motion of the car.

Acceleration due to gravity = g

Centripetal acceleration = $\frac{v^{2}}{R}$ , where v is the uniform speed of the car and R is radius of the track.

Effective acceleration $a_{e f f}$ is given by $a_{e f f} = \sqrt{{(g}^{2}} + ({\frac{v^{2}}{R})}^{2})$

Time period, T = 2 $π \sqrt{\frac{l}{g^{2} + \frac{v^{4}}{R^{2}}}}$ , where l = length of the pendulum

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