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A thin copper wire of length L increase ...

A thin copper wire of length L increase in length by 2 % when heated from `T_(1)` to `T_(2)`. If a copper cube having side 10 L is heated from `T_(1)` to `T_(2)` when will be the percentage change in
(i) area of one face of the cube
(ii) volume of the cube

Text Solution

Verified by Experts

(i) Area `A = 10 L xx 10 L = 100 L`
% change in area `= (DeltaA)/(A)xx100=2xx(DeltaL)/(L)xx100=2xx2%=4%`
(ii) Volume `V = 10Lxx10 L xx 10 L = 1000 L^(3)`
% change in volume `= (Delta V)/(V)xx100=3xx(DeltaL)/(L)xx100=3xx2% =6%`
Conclusion : The maximum percentage change will be observed in volume, lesser in area and the least (minimum) change will be observed in length or radius.
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