Two wires of different materials each of length `l` and cross sectional area 'A' are joined in series to form a composite wire. If their young's moduli are Y and 2Y, the total elongation produced by applying a force F to stretch the composite wire will be

Options

A. `(3FA)/(2Yl)`
B. `(2FA)/(3Yl)`
C. `(2FA)/(3AY)`
D. `(3Fl)/(2AY)`

Answer

D

Explanation

`l=l_(1)+l_(2)`
`=(FL)/(Ay)+(FL)/(A_(2)y)=(FL)/(Ay)[1+(1)/(2)]`
`l=(3)/(2) (FL)/(Ay)`.