Question

A wire of length 1 cm and a cube of side 1 cm of the same metal are heated through 1$C^o$ If the change in length of the wire is x cm then the change in volume of the cube is :

• A. $x{d}^{3}c{m}^3$
• B. $3xc{m}^3$
• C. $xc{m}^3$
• D. Indeterminate as data are insufficient

Answer 1

The correct option is B $3xc{m}^3$

$\delta \left(L\right)=L_0{\alpha }_0\delta \left(T\right)$
For wire, x= 1 ${\alpha }_0$(1)
thus, ${\alpha }_0$= x
V'= $L^{\prime 3}=L_0^3(1+{\alpha }_0\delta (T){)}^3$
Ignoring higher powers; $V^{\prime }=V_0(1+3{\alpha }_0(\delta \left(T\right)\left)\right)$
$\delta \left(V\right)=3{\alpha }_0\delta \left(T\right)$
For cube: $\delta \left(V\right)=3x\left(1\right)=3xc{m}^3$