The design of some 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. Find their lengths.
`(alpha_(Fe)=11 xx 10^(6).^(@)C^(-1),alpha_(Cu)=17 xx 10^(-6) .^(@)C^(-1))`

Options

A. 28.3 cm and 18.3 cm
B. 23.8 cm and 13.8 cm
C. 28.9 cm and 10.9
D. 27.5 cm and 14.5 cm

Answer

A

Explanation

Since a constant difference in length of 10 cm between an iron rod and a copper cylinder is required
`L_(Fe)-L_(Cu)0=10cm` ..(i)
or `DeltaL_(Fe)-DeltaL_(Cu)=O :. DeltaL_(Fe)=DeltaL_(Cu)`
i.e., linear expansion of iron rod = linear expansion of copper cylinder
`impliesL_(Fe)xxalpha_(Fe)xxDeltaT=L_(Cu)xxalpha_(Cu)xxDeltaT`
`implies(L_(Fe))/(L_(Cu))=(alpha_(Cu))/(alpha_(Fe))=(17)/(11)`
`:. (L_(Fe))/(L_(cu))=(17)/(11)` (ii)
From Eqs (i) and (ii) `L_(Fe)=28.3cm`,`L_(Cu)=18.3cm`.