For a given material, young's modulus is 2.6 times the rigidity modulus. The poisson's ratio is 
 

The fractional change in the longitudinal length is inversely correlated with the fractional change in the transverse length. The Poisson's ratio is the name of the proportionality constant. It is provided with respect to Youngs' modulus and rigidity modulus.

$\mathrm{\sigma }=-\frac{{\displaystyle \frac{∆\mathrm{d}}{\mathrm{d}}}}{{\displaystyle \frac{∆\mathrm{L}}{\mathrm{L}}}}$

$\mathrm{\sigma }=\frac{\mathrm{Y}}{2\mathrm{\eta }}-1$

$\mathrm{Y}=2.6\mathrm{\eta }$

$\mathrm{\sigma }=\frac{2.6\mathrm{\eta }}{2\mathrm{\eta }}-1=0.3$

Hence the correct answer is 0.3