A brass rod of length 2 m and corss-sectinal area `2.0 cm^(2)` is attached to end to a steel rod of length L and corss-sectinal area `1.0 cm^(2)`. The compound rod is subjected to equal and opposite pulls of magnitude `5 xx 10^(4) N` at its ends.
If the elongations of the two rods are equal, then the length of the steel rod L is `(Y_("brass") = 1.0 xx 10^(11) Nm^(-2)` and `y_("steel") = 2.0 xx 10^(11) Nm^(-2))`

Options

A. 1.5 m
B. 1.8 m
C. 1 m
D. 2 m

Answer

d

Explanation

`(Delta I)_(B) = (Delta I)_(s)`

or `((FI)/(AY))_(B) = ((FI)/(AY))_(s)`
or `((I)/(AY))_(B) = ((I)/(AY))_(S)`
`:. I_(s) = ((A_(S)Y_(S))/(A_(B)Y_(B))) I_(B) = ((1.0 xx 2.0 xx 10^(11))/(2.0 xx 1.0 xx 10^(11))) (2m) = 2m`