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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 = 100L^(2) rArr A prop L^(2)`
% change in area `= (Delta A)/(A) xx 100 = 2xx (Delta L)/( L) xx 100 = 2 xx 2% = 4%`
(ii) Volume V `=10L xx 10L xx 10 L = 1000 L^(3) rArr V prop L^(3)`
% change in volume `= (Delta v )/(V) xx 100 = 3 ( Delta L)/(L) = 3 xx 2% = 6%`
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