In Fig., AB is a 2 m long rod of negligible weight. It is supported at the ends by wires X and Yofequal length. Young's modulus for wire X is `2 xx 10^(11) N//m^(2)` and its area of cross-section 3 `mm^(2)` . For wire Y, Young's modulus is `1.4 xx 10^(11)" N//m^(2)` and its area of cross-section is 6 `mm^(2)`. A mass M is suspended at any point along the rod.

Distance of a point on the rod from A, such that the mass M suspended from it will result in equal stresses in wires X and Y, is:

Options

A. `8//5 ` m
B. `7//6` m
C. `4//3` m
D. `2//3` m

Answer

C

Explanation

` Y_(1) = 2xx 10^(11) Nm^(-2) A_(1) =3 mm^(2)`
`Y_(2) = 1.4 xx 10^(11) Nm^(-2) A_(2) = 6 mm^(2)`
`(F_(1))/(3) =(F_(2))/(6) :. (F_(1))/(F_(2)) = (1)/(2) (F_(1))/(F_(2)) = (2-x)/(x) =(1)/(2)`
4-2x =x 4=3x
`x = (4)/(3) ` m