Concepts Of Physics MCQ Edition [Volume 1]PhysicsSimple Harmonic Motion
A simple pendulum of length l is suspended from the ceiling of a car travelling with a speed v on a circular horizontal road of radius r . Determine the time period of small oscillations.
Options
- A2 l ( g^2 + v^4 r^2 )^ 1/2
- B2 l ( g^2 + v^2 r )^ 1/2
- C2 l g
- D2 l ( g^2 - v^4 r^2 )^ 1/2
Correct answer
A. 2 l ( g^2 + v^4 r^2 )^ 1/2
Step-by-step solution
In the frame of the car, the pendulum bob experiences a pseudo force (centrifugal force) in the horizontal direction due to the circular motion of the car. The centrifugal acceleration is a_c = v^2 r directed radially outward. The acceleration due to gravity g acts vertically downward. Since the horizontal and vertical accelerations are perpendicular to each other, the effective acceleration due to gravity g_ eff is given by: g_ eff = g^2 + a_c^2 = g^2 + ( v^2 r )^2 = ( g^2 + v^4 r^2 )^ 1/2 The time period of small