If M=mass of wire, `rho`=density of wire, R=radius of wire, r=change in radius, L=original length of wire and l=change in length, then poisson's ratio is given by

Options

A. `(Mr rho)/(piR^(3)l)`
B. `(Mr)/(piR^(2)lrho)`
C. `(Mr)/(piR^(3)rhol)`
D. `(Mr rho)/(piR^(2)l)`

Answer

C

Explanation

As we know that,
Poisson's ratio`=("Lateral strain")/("Longitudinal strain")`
`sigma=(r//R)/(l//L)=(rL)/(Rl)` . . . (i)
Also, `M=piR^(2)lrhoimpliesL=(M)/(piR^(2)rho)`
Putting this value of L in Eq. (i) we get
`sigma(r(M//piR^(2)rho))/(Rl)=(Mr)/(piR^(3)rhol)`