The Poisson’s ratio of a material is 0.5. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is:

Options

A. 0.01
B. 0.02
C. 0.025
D. 0.04

Answer

D

Explanation

Here `0.5 = (Delta r// r)/(Delta l//l) " or " 1/2 (Delta l)/(l) = (Delta r)/(r )`
` because A = pi r^2`
` therefore (Delta A)/(A) = 2 (Delta r)/(r )" or " 2 (Delta r)/( r) = 4 " or " (Delta r)/(r ) = 2%`
Thus` (Delta l)/(l) = 2 xx 2 = 4%`