Physics

Problem

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 : a.

L \left( 1 + \frac{2}{9} \frac{Mg}{\pi Y R^2} \right)

L \left( 1 + \frac{1}{9} \frac{Mg}{\pi Y R^2} \right)

L \left( 1 + \frac{1}{3} \frac{Mg}{\pi Y R^2} \right)

L \left( 1 + \frac{2}{3} \frac{Mg}{\pi Y R^2} \right)