The design of a physical instrument requires that there be a constant difference in length of 10 cm between an iron rod and a copper cylinder laid side by side at all temperatures. If `alpha_(Fe)=11xx10^-6^(@)//C` and `alpha_(cu)=17xx10^-6^(@)//C`, their lengths may be

Options

A. 28.3 cm, 18.3 cm
B. 23.8 cm, 13.8 cm
C. 23.9 cm, 10.9 cm
D. 27.5cm, 14.5 cm

Answer

A

Explanation

`l_(2)-l_(1)=l_(20)-l_(10)+(l_(2)alpha_(2)-l_(1)alpha_(1))DeltaT" to have"l_(2)-l_(1)=l_(20)-l_(10)rArrl_(2)alpha_(2)=l_(1)alpha_(1)`
`or,(l_(1)+10)(11xx10^(-6))=l_(1)(17xx10^(-6))or,11(l_(1))+110=17l_(1)`
`or,l_(1)=(110)/(6)=18.33" cm",l_(2)=28.33 " cm "`