If two rods of length L and 2L having coeffic | vedclass

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

Question

(C) The initial length of the combination is $L + 2L = 3L$.The change in length of the first rod is $\Delta L_1 = L \alpha \Delta t$.The change in len

Vedclass · Accepted Answer

$\frac{5}{3}\alpha$

Vedclass · Answer

(C) The initial length of the combination is $L + 2L = 3L$.The change in length of the first rod is $\Delta L_1 = L \alpha \Delta t$.The change in length of the second rod is $\Delta L_2 = (2L)(2\alpha) \Delta t = 4L \alpha \Delta t$.The total change in length of the composite rod is $\Delta L_{total} = \Delta L_1 + \Delta L_2 = L \alpha \Delta t + 4L \alpha \Delta t = 5L \alpha \Delta t$.The average coefficient of linear expansion $\alpha_{avg}$ is defined by the relation $\Delta L_{total} = L_{total} \alpha_{avg} \Delta t$.Substituting the values,we get $5L \alpha \Delta t = (3L) \alpha_{avg} \Delta t$.Solving for $\alpha_{avg}$,we get $\alpha_{avg} = \frac{5L \alpha \Delta t}{3L \Delta t} = \frac{5}{3}\alpha$.

If two rods of length $L$ and $2L$ having coefficients of linear expansion $\alpha$ and $2\alpha$ respectively are connected so that the total length becomes $3L$,the average coefficient of linear expansion of the composite rod equals:

Similar Questions

$A$ sphere floats on a liquid whose volume does not change with temperature. At temperatures $t_1$ and $t_2$,the fractions $f_1$ and $f_2$ of the sphere are submerged in the liquid,respectively. What is the coefficient of volume expansion of the sphere?

The length of a metal rod at $30^{\circ} C$ is $30 \ cm$. If its temperature is raised to $105^{\circ} C$,its length is increased by $0.027 \ cm$. Then the coefficient of linear expansion of the metal is

When a copper ball is heated,which of the following will show the maximum percentage increase?

The difference in length between two rods $A$ and $B$ is $60 \text{ cm}$ at all temperatures. If $\alpha_{A} = 18 \times 10^{-6} /^{\circ}\text{C}$ and $\alpha_{B} = 27 \times 10^{-6} /^{\circ}\text{C}$,the lengths of the two rods are:

The coefficients of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$ respectively. The lengths of the brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2 - l_1)$ is maintained the same at all temperatures,which one of the following relations is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module