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JEE Main 2015 · Other SHM Systems

Other SHM Systems question from JEE Main 2015

Q18JEE Main 2015Difficult

Other SHM Systems

A pendulum made of a uniform wire of cross sectional area AA has time period T.T. When an additional mass MM is added to its bob, the time period changes to TM.T_M. If the Young's modulus of the material of the wire is YY then 1Y\frac{1}{Y} is equal to:

(g=g = gravitational acceleration)

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Answer: (c)

  1. Added mass stretches the wire: ΔL=MgLAY\Delta L = \frac{MgL}{AY}, and T∝LT \propto \sqrt{L}.
  2. (TMT)2=L+ΔLL=1+MgAY\left(\frac{T_M}{T}\right)^2 = \frac{L + \Delta L}{L} = 1 + \frac{Mg}{AY}
  3. 1Y=[(TMT)2−1]AMg\frac{1}{Y} = \left[\left(\frac{T_M}{T}\right)^2 - 1\right]\frac{A}{Mg}, answer (c).
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