If the ratio of lengths, radii and Young's modulus of steel and brass wires shown in the figure are a, b and c respectively, the ratio between the increase in lengths of brass and steel wires would be Brass and steel wire would be

Options

A. `(b^(2)ac)/(2c)`
B. `(bc)/(2a^(2))`
C. `(ba^(2))/2c`
D. `a/(b^(2)c)`

Answer

D

Explanation

`l_(1)/l_(2) = a,r_(1)/r_(2)=b,E_(1)/E_(2) =c`
`E_(1) =F_(1)/A_(1) .l/(Deltal)`
`E_(2)=F_(2)/A_(2) . L_(2)/(Deltal_(2))`
`E_(1)/E_(2) = (F_(1)A_(2).l_(1)Deltal_(2))/(F_(2)A_(1).l_(2)Deltal_(1)`
Force acting on the steel wire
`T=F_(1)=2kg`
Forces acting on the brass wire
`F_(2)=T_(2)=T+2kg=4kg`
`therefore E_(1)/E_(2) =2/4 . pi_(2)^(2)/pi_(1)^(2) . l_(1)/l_(2) . (Deltal_(2))/(Deltal_(1)`
`therefore C= 1/2 1/b_(2).a (Deltal_(2))/(Deltal_(1))`
`therefore (Deltal_(1))/(Deltal_(2))=a/(2b^(2)c)`