JEE Main 2016 · 9 Apr · Shift 1 · Physics Q26

← JEE Main 2016 · 9 Apr · Shift 1

PhysicsSingle correct+4 / -1Question 26 of 90

A uniformly tapering conical wire is made from a material of Young's modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal :

L\left(1+\dfrac29\dfrac{Mg}{\pi YR^2}\right)

L\left(1+\dfrac13\dfrac{Mg}{\pi YR^2}\right)

L\left(1+\dfrac19\dfrac{Mg}{\pi YR^2}\right)

L\left(1+\dfrac23\dfrac{Mg}{\pi YR^2}\right)

Answer and worked solution

Official answer: B

At distance y from the top the radius is $R\left(1+\frac{2y}L\right)$ , and
$\Delta L=\int_0^L\frac{Mg\,dy}{\pi YR^2(1+2y/L)^2}=\frac{MgL}{\pi YR^2}\cdot\frac12\left(1-\frac13\right)=\frac{MgL}{3\pi YR^2}.$

Topics:Hooke's law and elastic moduli

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JEE Main 2016 · 9 Apr · Shift 1, Physics question 26