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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^(2)`.
Percentage change in area `= (DeltaA)/(A)xx100`
`=2xx(DeltaL)/(L)xx100 2 xx 2%= 4%`
`"(" :'(DeltaA)/(L)= (Delta100)/(100)+2(DeltaL)/(L)= 0 + 2(DeltaL)/(L)= 2(DeltaL)/(L) ")"`
Note :- Constants do not have any error in them.
(ii) Volume `V= 10Lxx10Lxx10L=1000L^(3)`
percentage change in volume `=(DeltaV)/(V)xx100=3(DeltaL)/(L)`
`=3xx2%=6%`
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