Two rods of same mass and same length lo but having different coefficient of expansions $\mathrm{\alpha }$ and 3$\mathrm{\alpha }$ are joined at P (see figure). System is placed on frictionless surface. If
temperature of whole system is changed by $∆\mathrm{T}$, the displacement of junction point is
 

• A

  ${\mathrm{l}}_{\circ }\mathrm{\alpha \Delta T}$

• B

  $2{\mathrm{l}}_{\circ }\mathrm{\alpha \Delta T}$

• C

  $\frac{{\mathrm{l}}_0\mathrm{\alpha \Delta T}}{2}$

• D

  $\frac{3}{4}{\mathrm{l}}_0\mathrm{\alpha \Delta T}$