Question

Three aluminium rods of equal length form an equilateral triangle $ABC$. Take $O$ (mid point of rod $BC$) as the origin. The increase in Y-coordinate of center of mass per unit change in temperature of the system is given as $x\times {10}^{-6}m{/}^{\circ }C$. Find $x$. Assume the length of each rod is $2m$, and ${\alpha }_{al}=4\sqrt{3}\times {10}^{-6}{/}^{\circ }C$.

Answer 1

Distance of O from the center of mass=Radius of inscribed circle in the triangle=$\frac{\sqrt{3}}{6}L=R$

Thus change in this radius per unit change in temperature=$R\alpha$

$=\frac{\sqrt{3}}{6}L\times 4\sqrt{3}\times {10}^{-6}{/}^{\circ }C=4\times {10}^{-6}m{/}^{\circ }C$