NEET Physics Question - Oscillation - Angular SHM and Simple Pendulum

Assertion (A): For a physical pendulum if distance of point of suspension from centre of mass increases time period first decreases then increases.

Reason (R): For a physical pendulum there is some distance from centre of mass at which frequency of oscillation is maximum.

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:

The time period of a physical pendulum is \(T = 2pi sqrt{(I_{CM} + mL^2)/(mgL)}\). Analyzing this function, \(T\) has a minimum value at \(L = sqrt{I_{CM}/m}\). This minimum time period corresponds to a maximum frequency. Thus, as \(L\) increases, \(T\) first decreases to a minimum and then increases. Both Assertion (A) and Reason (R) are true, and R correctly explains A.

Rankers Physics

Physical pendulum and time period

Solution:

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