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Question

An Object of mass m is suspended at the end of a massless wire of length L and area of cross-section A, Young modulus of the material of the wire is Y. If the mass is pulled down Slightly, its frequency of oscillation along the vertical direction is:

A
f=12πmLYA
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B
f=12πYAmL
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C
f=12πmAYL
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D
f=12πYLmA
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Solution

The correct option is B f=12πYAmL
An elastic wire can be treated as a spring and its spring constant is given as
k=YAL ⎢ ⎢ ⎢ ⎢Y=(FA)(Δll0)⎥ ⎥ ⎥ ⎥
Thus, frequency of oscillation will be
f=12πkm=12πYAmL
Hence, (B) is the right option.

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