A wire of length L and radius r is loaded with a weigth Mg. If y and `sigma` denote the Youngs modulus and Poisson's ratio of the material of the wire respectively. Then the decreases in the radius of the wire is given by

Options

A. `Delta r = (sigma pi r)/(Mg Y)`
B. `Delta r = (M g r)/(pi sigma Y)`
C. `Delta r = (Mg sigma)/(pi r Y)`
D. `Delta r = (Mg Y)/(pi r sigma)`

Answer

C

Explanation

`Y = (MgL)/(pir^(2) (Delta L)) :. (Delta L)/(L) = (Mg)/(pi r^(2) Y)` …(1)
and `sigma - ((Delta D)/(D))/((Delta L)/(L)) = ((Delta r)/(r ))/((Delta L)/(L))`
`:. (Delta r)/(r ) = sigma((Delta L)/(L)) = sigma.(Mg)/(pi r^(2) Y)` …from (1)
`:. Delta r = sigma . (Mg)/(pi r^(2) Y) xx r = (sigma Mg)/(pi r Y)`