A meter stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency $$f0$$. If the bottom half of the stick were cut off if its new frequency of small oscillation is found to be $$xf0$$. The value of x is $$_____$$.

Question

A meter stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency $$f0$$. If the bottom half of the stick were cut off if its new frequency of small oscillation is found to be $$xf0$$. The value of x is $$_____$$.

Infinity Learn · Accepted Answer

We use $$f0=12$$$$π$$mglIwhere l is distance between point of suspension and centre of mass of the body.Thus, for the stick of length L and mass m frequency $$isf0=12$$$$π$$m⋅g⋅$$L2mL2/12=12$$$$π$$$$6gLwhen$$ bottom half of the stick is cut off we $$usef1=12$$$$π$$$$m2$$⋅g⋅$$L4m2(L/2)212=12$$π×$$12gL=2f0Hence$$ x $$=$$ $$2$$.

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A meter stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency f₀. If the bottom half of the stick were cut off if its new frequency of small oscillation is found to be $\sqrt{x} f_{0}$ . The value of x is _____.

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Applications of SHM

Remember concepts with our Masterclasses.

A meter stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency f0. If the bottom half of the stick were cut off if its new frequency of small oscillation is found to be xf0. The value of x is _____.

We use f0=12πmglIwhere l is distance between point of suspension and centre of mass of the body.Thus, for the stick of length L and mass m frequency isf0=12πm⋅g⋅L2mL2/12=12π6gLwhen bottom half of the stick is cut off we usef1=12πm2⋅g⋅L4m2(L/2)212=12π×12gL=2f0Hence x = 2.

Ready to Test Your Skills?

free study material

A meter stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency f₀. If the bottom half of the stick were cut off if its new frequency of small oscillation is found to be $\sqrt{x} f_{0}$ . The value of x is _____.