When a rubber cord is stretched, the change in volume with respect to change in its linear dimensions is negligible. The Poisson's ratio for rubber is

Options

A. 1
B. 0.25
C. 0.5
D. 0.75

Answer

c

Explanation

As volume, `V = pi r^(2) I`
`implies (Delta V)/(V) = (Delta (pi r^(2) I))/(pi r^(2) I) = (r^(2) Delta I + 2 r I Delta r)/(r^(2) I)`
or `(Delta V)/(V) =(Delta l)/(l) + (2 Delta r)/(r )`
`:' (Delta V)/(V)` is negligible
`:. (Delta I)/(I) = (-2 Delta r)/(r )`
Now, poisson's ratio, `sigma = - (Delta r // r)/((Delta l)/(l)) = - (Delta r // r)/(-2 (Delta r)/(r )) = 0.5`