Question

Two uniform rods of equal length $\left(l_n\right)$ and equal mass have the coefficient of linear expansion $\alpha$ and $2\alpha$ are placed in contact on a smooth horizontal surface as shown in the figure. The temperature of the system is ${\theta }^{0}C$. Now the temperature is increased by $\Delta {\theta }^{0}C$.The junction of the rods will shift its initial position by:

• A. $\frac{l_0\alpha \Delta \theta }{2}$
• B. $\frac{l_0\alpha \Delta \theta }{3}$
• C. $\frac{l_0\alpha \Delta \theta }{4}$
• D. $\frac{l_0\alpha \Delta \theta }{6}$

Answer 1

The correct option is A $\frac{l_0\alpha \Delta \theta }{2}$

Expansion in rod for linear coefficient $\alpha$

$\frac{△l}{l}=\alpha △\theta$

With $2\alpha$,

$\frac{△l}{l}=2\alpha △\theta$

So, $△l$ from left side $\Rightarrow △l_L=l\alpha △\theta$

$△l$ from right side $\Rightarrow △l_R=2l\alpha △\theta$

So, the junction will shift $\frac{l_o\alpha △\theta }{2}$ in the right direction.