Concepts Of Physics MCQ Edition [Volume 1]PhysicsSimple Harmonic Motion
A simple pendulum of length l and mass m is suspended from the ceiling of a car travelling with a speed v on a circular horizontal road of radius r . Determine the tension in the string when it is at rest with respect to the car.
Options
- Am ( g^2 + v^4 r^2 )^ 1/2
- Bm ( g^2 - v^4 r^2 )^ 1/2
- Cm ( g^2 + v^2 r )^ 1/2
- Dm ( g + v^2 r )
Correct answer
A. m ( g^2 + v^4 r^2 )^ 1/2
Step-by-step solution
In the frame of reference of the car, the forces acting on the pendulum bob are the gravitational force mg acting vertically downwards, the centrifugal force mv^2 r acting horizontally outwards, and the tension T in the string. Since the pendulum is at rest with respect to the car, it is in equilibrium in the car's frame. The tension T in the string must balance the resultant of the gravitational force and the centrifugal force. As the gravitational force and the centrifugal force are perpendicular to each other, t