When the temperature of a metal wire is increased from 0^oC to 10^oC, its length increases by 0.02%. The percentage change in its mass density will be closest to :

Given, ${{\Delta L} \over L}$ = 0.02% <br><br>We know, $\Delta$L = L$\alpha$$\Delta$T <br><br>$\Rightarrow$ ${{\Delta L} \over L} = \alpha \Delta T$ = 0.02 <br><br>Also, $\beta$ = 2$\alpha$ <br><br>$\Rightarrow$ $\beta \Delta T = 2\alpha \Delta T$ = 0.04 <br><br>Density($\rho$) = ${M \over {AL}}$ <br><br>$\Rightarrow$ $${{\Delta \rho } \over \rho } = {{\Delta M} \over M} - {{\Delta A} \over A} - {{\Delta L} \over L}$$ ( ${{\Delta M} \over M}$ = 0 as M = constant) <br><br>$\Rightarrow$ ${{\Delta \rho } \over \rho } = {{\Delta A} \over A} + {{\Delta L} \over L}$ <br><br>= $\beta \Delta T + \alpha \Delta T$ <br><br>= 0.04 + 0.02 = 0.06 %