Question:
Two different wires having lengths \(L_1\) and \(L_2\), and respective temperature coefficient of linear expansion \(\alpha_1\) and \(\alpha_2\), are joined end-to-end. Then the effective temperature coefficient of linear expansion is :
Two different wires having lengths \(L_1\) and \(L_2\), and respective temperature coefficient of linear expansion \(\alpha_1\) and \(\alpha_2\), are joined end-to-end. Then the effective temperature coefficient of linear expansion is :
Show Hint
The total expansion of the joined wire is the sum of the individual expansions: \(\Delta L = \Delta L_1 + \Delta L_2\); divide by the total length and \(\Delta T\).
Updated On: Nov 5, 2026
- \(2\sqrt{\alpha_1\alpha_2}\)
- \(4\,\frac{\alpha_1\alpha_2}{\alpha_1+\alpha_2}\,\frac{L_2L_1}{(L_2+L_1)^2}\)
- \(\frac{\alpha_1+\alpha_2}{2}\)
- \(\frac{\alpha_1L_1+\alpha_2L_2}{L_1+L_2}\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Total length L = \(L_1 + L_2\).
For a temperature rise \(\Delta T\): \(\Delta L_1 = L_1\alpha_1\Delta T\) and \(\Delta L_2 = L_2\alpha_2\Delta T\).
For the combination, \(\Delta L = L\alpha_{eff}\Delta T = (L_1+L_2)\alpha_{eff}\Delta T\).
Since \(\Delta L = \Delta L_1 + \Delta L_2\): \((L_1+L_2)\alpha_{eff} = \alpha_1L_1 + \alpha_2L_2\).
\(\alpha_{eff} = \frac{\alpha_1L_1+\alpha_2L_2}{L_1+L_2}\).
Answer: (4) \(\frac{\alpha_1L_1+\alpha_2L_2}{L_1+L_2}\)
For a temperature rise \(\Delta T\): \(\Delta L_1 = L_1\alpha_1\Delta T\) and \(\Delta L_2 = L_2\alpha_2\Delta T\).
For the combination, \(\Delta L = L\alpha_{eff}\Delta T = (L_1+L_2)\alpha_{eff}\Delta T\).
Since \(\Delta L = \Delta L_1 + \Delta L_2\): \((L_1+L_2)\alpha_{eff} = \alpha_1L_1 + \alpha_2L_2\).
\(\alpha_{eff} = \frac{\alpha_1L_1+\alpha_2L_2}{L_1+L_2}\).
Answer: (4) \(\frac{\alpha_1L_1+\alpha_2L_2}{L_1+L_2}\)
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
- A particle starts with an initial velocity of 10.0 m/s along x-direction and accelerates uniformly at the rate of 2.0 m/s$^2$. The time taken by the particle to reach the velocity of 60.0 m/s is
View More Questions
Top JEE Main thermal properties of matter Questions
- The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are \( 8 \, \Omega \) and \( 10 \, \Omega \) respectively. After inserting in a hot bath of temperature \( 400^\circ \text{C} \), the resistance of the platinum wire is:
- An elastic spring under tension of 3 N has a length a. Its length is b under tension 2 N. For its length (3a – 2b), the value of tension will be_____ N.
- Two persons pull a wire towards themselves. Each person exerts a force of $200 \, \text{N}$ on the wire. Young’s modulus of the material of the wire is $1 \times 10^{11} \, \text{N m}^{-2}$. Original length of the wire is $2 \, \text{m}$ and the area of cross-section is $2 \, \text{cm}^2$. The wire will extend in length by ______ $\mu \text{m}$.
- Statement--1: Liquid pressure is only exerted on solid surfaces in contact and is exerted in between the layers of liquid. Statement--2: Surface tension arises due to difference in potential energy of molecules in the bulk of liquid and at the surface.
- A $100\, m$ long wire having cross-sectional area $625 \times 10^{-4} \, m ^2$ and Young's modulus is $10^{10} Nm ^{-2}$ is subjected to a load of $250 \, N$, then the elongation in the wire will be:
View More Questions
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
View More Questions