The rods of length L_1 and L_2 are made of ma | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the lengths of the rods at temperature $T$ be $L_1$ and $L_2$. At a temperature $T + \Delta T$,the new lengths are $L_1' = L_1(1 + \alpha_1 \D

Vedclass · Accepted Answer

$\frac{L_1}{L_2} = \frac{\alpha_2}{\alpha_1}$

Vedclass · Answer

(B) Let the lengths of the rods at temperature $T$ be $L_1$ and $L_2$. At a temperature $T + \Delta T$,the new lengths are $L_1' = L_1(1 + \alpha_1 \Delta T)$ and $L_2' = L_2(1 + \alpha_2 \Delta T)$. The difference between the lengths is independent of temperature,so $L_1' - L_2' = L_1 - L_2$. Substituting the expressions: $L_1(1 + \alpha_1 \Delta T) - L_2(1 + \alpha_2 \Delta T) = L_1 - L_2$. Expanding this,we get $L_1 + L_1 \alpha_1 \Delta T - L_2 - L_2 \alpha_2 \Delta T = L_1 - L_2$. Subtracting $(L_1 - L_2)$ from both sides,we get $L_1 \alpha_1 \Delta T = L_2 \alpha_2 \Delta T$. Since $\Delta T 
eq 0$,we have $L_1 \alpha_1 = L_2 \alpha_2$. Therefore,$\frac{L_1}{L_2} = \frac{\alpha_2}{\alpha_1}$.

The rods of length $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are $\alpha_1$ and $\alpha_2$ respectively. If the difference between the two lengths is independent of temperature,then:

Similar Questions

When a copper sphere is heated,in which of the following will the maximum percentage change be observed?

$A$ sheet of steel at $20^{\circ} C$ has dimensions as shown in the figure. If the coefficient of linear expansion for steel is $10^{-5} {^{\circ} C}^{-1}$, what is the change in the area at $60^{\circ} C$ (in $\text{ cm}^2$)?

On what value does the coefficient of linear expansion $\alpha_l$ depend? Write its unit.

The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6} /{ }^{\circ} C$ and in a steel vessel is $144 \times 10^{-6} /{ }^{\circ} C$. If $\alpha$ for steel is $12 \times 10^{-6} /{ }^{\circ} C$, then the coefficient of linear expansion $\alpha$ for glass is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module