Two simple pendulums having lengths 
and 
with negligible string mass undergo angular displacements 
and 
, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?
Text Solution
Verified by ExpertsA
Angular Frequency: The angular frequency ( 
) of a simple pendulum is given by:
where 
is the acceleration due to gravity and 
is the pendulum length.
Angular Acceleration: The angular acceleration ( 
) can be expressed in terms of angular displacement 
and angular frequency:
Equating Angular Accelerations: Since the angular accelerations of the two pendulums are equal, we equate them:
Simplifying the Expression: By canceling out 
on both sides, we derive:
Thus, the correct expression that relates the displacements and lengths of the pendulums is 
.
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