If the ratio of lenghts, radi and Young's moduli of steel and brass wires are `a,b` and `c` respectively their respective loads are in the ratio `3:2` then the corresponding ratio of increases in their lenghts would be

Options

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

Answer

B

Explanation

`Delta l = (FL)/(AY) rArr (Delta l_(S))/(Delta l_(B)) = ((F_(S))/(F_(B))) ((L_(S))/(L_(B))) ((A_(B))/(A_(S))) ((Y_(B))/(Y_(S)))`
`= ((3)/(2)) (a) ((1)/(b^(2))) ((1)/(c)) = (3a)/(2b^(2)c)`