A wire of length 1 cm and a cube of side 1 cm of the same metal are heated through 1Co If the change in length of the wire is x cm then the change in volume of the cube is :
xd3cm3
3xcm3
Indeterminate as data are insufficient
xcm3
A
xd3cm3
B
3xcm3
C
Indeterminate as data are insufficient
D
xcm3
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Solution
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δ(L)=L0α0δ(T) For wire, x= 1 α0(1) thus, α0= x V'= L′3=L30(1+α0δ(T))3 Ignoring higher powers; V′=V0(1+3α0(δ(T))) δ(V)=3α0δ(T) For cube: δ(V)=3x(1)=3xcm3
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