If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are `a, b` and `c` respectively then the corresponding ratio of increase in their lengths is

Options

A. `(2a^2c)/(b)`
B. `(3a)/(2b^2c)`
C. `(2ac)/(b^2)`
D. `(3c)/(2ab^2)`

Answer

B

Explanation

`T_S=3mg`
`(3mg)/(A_S)=y_Sxx(trianglel_S)/(l_S)`
`(2mg)/(A_b)=y_bxx(trianglel_b)/(l_b)`
`(trianglel_S)/(trianglel_b)=(3)/(2)xx(l_S)/(l_b)xx(A_b)/(l_b)xx(A_b)/(A_S)xx(y_b)/(y_S)=(3)/(2)xx(a)/(b^2c)`