The radii and Young's moduli of two uniform wires A and B are in the ratio 2:1 and 1: 2 respectively. Both. wires are subjected to the same longitudinal force. If the increase in length of the wire A is one percent, the percentage increase in length of the wire B is

Options

A. 1
B. 1.5
C. 2
D. 3

Answer

C

Explanation

Change in length,`Delta l=(Fl)/(AE)`
Longitudinal forces is applied
`(Deltax_(1))/(Deltax_(2)) =[r_(1)/r_(2)]^(2) [Y_(2)/Y_(1)]`
`1/(Deltax_(2)) =[1/2]^(2) [2/1]=1/4 xx 2/1 =1/2`
`therefore Deltax_(2)=2%`