Question

The two bars below are made of the same metal. Bar $2$ is half as long as bar $1$. Each is heated so that its temperature goes up by ${100}^{o}C$.
How do their changes in length compare?

• A. The bars change length by the same amount
• B. Bar $1$ changes length by twice as much as bar $2$
• C. Bar $2$ changes length by twice as much as bar $1$
• D. Bar $1$ changes length by four times as much as bar $1$
• E. Bar $1$ changes length by just slightly more than bar $1$ (much less than twice as much)

Answer 1

The correct option is B Bar $1$ changes length by twice as much as bar $2$

Given : $L_1=2L_2$

Change in length of the bar due to increase in temperature $\Delta L=L\alpha \left(\Delta T\right)$

$⟹$ $\Delta L\propto L$ $(\alpha ,\Delta T=constant)$

$⟹$ $\frac{\Delta L_1}{\Delta L_2}=\frac{L_1}{L_2}=2$

Hence bar 1 changes its length by twice as much as bar 2.