Verified Solution • 2025–26 Session moderate

QJEEM20Ph9e06: JEE Main 2020 Physics - Class 11 JEEM20Ph9e06 Solution: An object of mass m is suspended at the end of a massless wire…

An object of mass m is suspended at the end of a massless wire of length L and area of crosssection 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 :

Multiple Choice Options

  • A f=12πYAmLf = {1 \over {2\pi }}\sqrt {{{YA} \over {mL}}}
  • B f=12πmLYAf = {1 \over {2\pi }}\sqrt {{{mL} \over {YA}}}
  • C f=12πYLmAf = {1 \over {2\pi }}\sqrt {{{YL} \over {mA}}}
  • D f=12πmAYLf = {1 \over {2\pi }}\sqrt {{{mA} \over {YL}}}

Step-by-Step Verified Solution

An elastic wire can be treated as a spring with

k = YAl{{YA} \over l}

T = 2πmk2\pi \sqrt {{m \over k}}

⇒\Rightarrow f = 12πkm{1 \over {2\pi }}\sqrt {{k \over m}} = 12πYAml{1 \over {2\pi }}\sqrt {{{YA} \over {ml}}}

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