Question

Two rods of same mass and same length $l_0$ but having different coefficient of expansions $\alpha$ and $3\alpha$ are joined at P (see figure). System is placed on frictionless surface. If temperature of whole system is changed by $△T,$ the displacement of junction point is

• A. $l_0\alpha △T$
  
• B. $2l_0\alpha △T$
  
• C. $\frac{l_0\alpha △T}{2}$
  
• D. $\frac{3}{4}{l}_0\alpha △T$

Answer 1

The correct option is C $\frac{l_0\alpha △T}{2}$


Net force on the system is zero hence displacement of the centre of mass of the system will be zero. Let x be the shift in P, then
$m\left(\frac{l_0}{2}\right(1+\alpha △T)+x)=m\left(\frac{l_0}{2}\right(1+3\alpha △T)-x)\Rightarrow x=\frac{l_0\alpha △T}{2}$