Two simple pendulums having lengths l1 and l2 with negligible string mass undergo angular displacements 1 and 2, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?
- 1 l2 = 2 l1
- 1 l1 = 2 l2
- 1 l22 = 2 l12
- 1 l12 = 2 l22
Answer
(1) 1 l2 = 2 l1
Solution
Restoring torque on a simple pendulum: = -mgl -mgl
Moment of inertia about the point of suspension: I = ml2
= I = - gl
Equal angular accelerations: gl1 1 = gl2 2
1 l2 = 2 l1
Answer: (1)