NEET Physics Question - Oscillation - Angular SHM and Simple Pendulum

Assertion (A): For large angle in simple pendulum \(T > 2\pi \sqrt{\frac{l}{g}}\)

Reason (R): \(sin \theta < \theta\), if the restoring force. \(mg sin \theta\) is replaced by \(mg \theta\), this amounts to effective reduction in g for large angle, hence an increase in T.

Both (A) & (R) are true and the (R) is the correct explanation of the (A)

Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(A) is true but (R) is false

Both (A) and (R) are false

Solution:

Assertion (A) is true: The period of a simple pendulum increases for large amplitudes compared to the small angle approximation. Reason (R) is true: For large angles, \(sin \theta < \theta\). This makes the actual restoring force smaller than the linear approximation, effectively reducing the 'g' and thereby increasing the period \(T\). (R) correctly explains (A).

Rankers Physics

Simple pendulum period for large angles

Solution:

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