A steel wire and a copper wire of equal length and equal cross sectional area are joined end to end and the combination is subjected to a tension. Find the ratio of a. The stresses developed in the two wire and b. the strains developed. Y of steel `=2xx10^11Nm^-2`. Y of copper `=1.3xx10^11 Nm^-2`.

Answer

A, B, C

Explanation

Given that `L_(steel)=L_(Cu)`
and `A_(steel)=A(Cu)`
`a. (stress of Cu)/(Strees of Steel)=(F_(Cu)A_(Steel))/A_(Cu)F_(Steel))`
`F_(Cu)/F_(Steel)=1`
`[because F_(Cu)=F_(Steel)]`
b. Strain`=(/_\L_(Steel))/(/_\Lcu)`
`=(F_(Steel)L_(Steel)A_(cu)Y_(cu))/(A_(Steel)Y_(Steel)F_(cu)I_(cu))`
`[L_(cu)=L_(Steel):A_(cu)=A_(Steel)]`
`rarr Y_(cu)/Y_(Steel)=(1.3xx10^11)/(2xx10^11)`
`rarr /_\L_(Steel)/(/_\I_(cu)=13/20`
`rarr (/_\_(cu))/(/_\L_(Steel)=20/13`