# Thermal Expansion

## Trending Questions

**Q.**Charges Q1 and Q2 are at points A and B of a right angle triangle OAB see figure. The resultant electric feild at point O is perpendicular to the hypotenuse, then Q1/Q2 is proportional to :

- x31x32
- x2x1
- x1x2
- x22x21

**Q.**The equation of an equipotential line in an electric field is y=2x, then the electric field strength vector at (1, 2) may be :

- 4^i+3^j
- 4^i+8^j
- 8^i+4^j
- −8^i+4^j

**Q.**The coefficient of linear expansion of steel and brass are 11×10−6/∘C and 19×10−6/∘C, respectively. If their differences in lengths at all temperatures has to kept constant at 30 cm, their lengths at 0∘C should be

- 71.25 cm and 41.25 cm
- 82 cm and 52 cm
- 92 cm and 62 cm
- 62.25 cm and 32.25 cm

**Q.**

The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis passing from the edge of the disc and normal to the disc is

**Q.**A physical quantity X is related to four measurable quantities a, b, c and d as follows X=a2b3c5/2d−2

The percentage error in the measurement of a, b, c and d are 1%, 2%, 2% and 4% respectively. What is the percentage error in quantity X?

- 21%
- 17%
- 23%
- 15%

**Q.**Two wires of same length and radius, are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y1 and Y2. The combination behaves as a single wire whose Young's modulus is :

- Y=Y1Y22(Y1+Y2)
- Y=2Y1Y23(Y1+Y2)
- Y=Y1Y2Y1+Y2
- Y=2Y1Y2Y1+Y2

**Q.**

Two different wires having lengths ${\mathrm{L}}_{1}$ and ${\mathrm{L}}_{2}$, and respective temperature coefficient of linear expansion ${\mathrm{\u0251}}_{1}$ and ${\mathrm{\u0251}}_{2}$, are joined end-to-end. Then the effective temperature coefficient of linear expansion is:

$[{\mathrm{\u0251}}_{1}{\mathrm{L}}_{1}+{\mathrm{\u0251}}_{2}{\mathrm{L}}_{2}]/[{\mathrm{L}}_{1}+{\mathrm{L}}_{2}]$

$2\sqrt{{\mathrm{\u0251}}_{1}{\mathrm{\u0251}}_{2}}$

$4\left[\right({\mathrm{\u0251}}_{1}{\mathrm{\u0251}}_{2})/[{\mathrm{\u0251}}_{1}+{\mathrm{\u0251}}_{2}\left]\right)][({\mathrm{L}}_{2}{\mathrm{L}}_{1}/{({\mathrm{L}}_{2}+{\mathrm{L}}_{1})}^{2}]$

$[{\mathrm{\u0251}}_{1}+{\mathrm{\u0251}}_{2}]/2$

**Q.**Co-efficient of linear expansion of brass and steel rods are α1 and α2 respectively. Lengths of brass and steel rods are L1 and L2 respectively. If (L2−L1) is maintained same at all the temperatures, which one of the following relations holds good?

- α1L1=α2L2
- α1L22=α2L21
- α1L2=α2L1
- α21L2=α22L1

**Q.**Two rods of different materials having coefficients of thermal expansion α1, α2 and Young's modulii Y1, Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If α1:α2=2:3 and thermal stresses developed in the two rods are equal, then Y1:Y2 is equal to

- 2:3
- 1:1
- 3:2
- 4:9

**Q.**When the temperature of a rod increases from T to T+ΔT, the moment of inertia of the rod about an axis increases from I to I+ΔI. If the coefficient of linear expansion of rod is α, then find the ratio ΔII

- ΔTT
- 2ΔTT
- αΔT
- 2αΔT

**Q.**A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27 ∘C. What is the change in the diameter of the hole when the sheet is heated to 227 ∘C ?

[ α=1.70×10−5/ ∘C ].

- 1.44×10−2 cm
- 1.96×10−2 cm
- 1.78×10−2 cm
- 1.28×10−2 cm

**Q.**A seconds pendulum clock has a steel wire. The clock shows correct time at 25∘C. How much time does the clock lose or gain in one week, when the temperature is increased to 35∘C ? (αsteel=1.2×10−5/∘C)

- 5.18 s gain
- 5.18 s lose
- 36.28 s gain
- 36.28 s lose

**Q.**A pendulum has time period T in air. When it is made to oscillate in water, it acquired a time period T′=√2T. The specific gravity of the pendulum bob is equal to

- 2
- None of these

**Q.**Two rods of different materials and of equal cross-sectional areas and length 1 m are joined face to face at one end and their free ends are fixed to rigid walls. If the temperature of the surrounding is increased by 30 ∘C, the magnitude of the displacement of the joint of the rods is :

[ α1=2×10−5 ∘C−1, α2=5×10−5 ∘C−1,

Y1=2×1010 N/m2, Y2=1010 N/m2 ]

- 15×10−5 m
- 12×10−5 m
- 10×10−5 m
- 18×10−5 m

**Q.**Two rods, one of aluminum and the other made of steel, having initial lengths l1 and l2 are connected together to form a single rod of length l1+l2. The co-efficients of linear expansion for aluminum and steel are αa and αs respectively. If the length of each rod increases by the same amount when their temperature are raised by t∘C, then find the ratio l1(l1+l2)

**Q.**Two straight metallic strips each of thickness t and length L are riveted together. Their coefficients of linear expansion are α1 and α2. If they are heated through temperature Δθ, the bimetallic strip will bend to form an arc of radius

- t(α1+α2)Δθ
- t(α2−α1)Δθ
- t2(α1+α2)Δθ
- t2(α2−α1)Δθ

**Q.**A bimetallic strip is made of two metal strips A and B, having coefficient of linear expansions αA and αB . If αA>αB, which of the following describes the behaviour of the bimetallic strip when heated?

- It will bend but will not elongate.
- It will bend with the strip B on the outer side.
- It will bend with the strip A on the outer side.
- No bending at all.

**Q.**A rod of length 20 cm is made of metal. It expands by 0.075 cm when its temperature is raised from 0∘C to 100∘C. Another rod of a different metal B having the same length expands by 0.045 cm for the same change in temperature. A third rod of the same length is composed of two parts one of metal A and the other of metal B. Now, the rod expands by 0.06 cm for the same change in temperature. The portion made of metal A has the length (in cm)

**Q.**

A pendulum clock gives correct time at 20∘ C at a place where g = 9.800 ms−2. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where g 9.788 ms−2. At what temperature will it give correct time ? Coefficient of linear expansion of steel =12×10−6 ∘C−1

**Q.**What is the effect of temperature on elasticity ? State reason .

**Q.**Two bodies of equal mass m are heated at a uniform rate under identical conditions. Their change in temperatures shown below. Then

(i) the ratio of melting points of the substances is 1.5.

(ii) the ratio of their latent heats is 0.75.

(iii) the ratio of specific heat of two substances is 0.33 in solid state.

(iv) the ratio of specific heat of two substances is 0.5 in liquid state.

- (iii), (iv)
- (ii), (iii)
(i), (iii)

- All

**Q.**The length of wire, when M1 is hung from it is l1 and is l2 with both M1 and M2 hanging. The natural length of wire is

- M1M2(l1−l2)+l1
- M2l1−M1l2M1+M2
- l1+L22
- √l1L2

**Q.**A uniform copper rod of length 50 cm and diameter 3 mm is kept on a frictionless horizontal surface at 20 ∘C. The coefficient of linear expansion of copper is 2×10−5 ∘C−1 and Young's modulus is 1.2×1011 N/m2. The copper rod is heated to 100 ∘C, Then, the tension developed in the copper rod is

- 12×103 N
- 18×103 N
- Zero
- 36×103 N

**Q.**A uniform thermometer scale is at steady state with its 0 cm mark at 20 ∘C and 100 cm mark at 100 ∘C. Temperature of the 60 cm mark is

- 48 ∘C
- 68 ∘C
- 52 ∘C
- 58 ∘C

**Q.**A bimetallic strip consists of metals X and Y. It is mounted rigidly at the base as shown in the figure. The metal X has a higher coefficient of expansion than metal Y. When the bimetallic strip is placed in a cold bath,

- It will bend towards right.
- It will bend towards left.
- It will not bend but shrink.
- It will neither bend nor shrink

**Q.**A metal rod having linear expansion coefficient 2 ×10−5°C−1 has a length of 1 m at 20∘C. The temperature at which it is shortened by 1 mm is

- –15°C
- –20°C
- –30°C
- –25°C

**Q.**Three rods of material X and three of material Y are connected as shown in figure. All the rods are identical in length and cross-sectional area. If the end A is maintained at 60∘C and the junction E at 10∘C, calculate the temperature at the junction B. The thermal conductivity of X is 800 Wm−1∘C−1 and that of Y is 400 Wm−1∘C−1.

- 35∘C
- 40∘C
- 45∘C
- 50∘C

**Q.**

The coefficient of linear expansion of iron is ${10}^{-5}/{}^{\circ}C$. The volume of an iron cube, $5cm$ on edge will increase by what amount if it is heated from $10\xb0\mathrm{C}$ to $60\xb0\mathrm{C}$?

$0.1875{\mathrm{cm}}^{3}$

$0.00375{\mathrm{cm}}^{3}$

$0.0225{\mathrm{cm}}^{3}$

$0.0625{\mathrm{cm}}^{3}$

**Q.**A brass rod and a lead rod each 80 cm long at 0 ∘C are clamped together at one end with their free ends coinciding. The separation the of free ends of the rods, if the system is placed in a steam bath is

[ αbrass=18×10−6/ ∘C and αlead=28×10−6/ ∘C and temperature of steam =100∘C ]

- 0.2 mm
- 0.8 mm
- 1.4 mm
- 1.6 mm

**Q.**A uniform rod of length 2L, area of cross section A and Youngs modulus Y is lying at rest under the action of three forces as shown. Choose the correct statement.

- The stress at any cross section in section BC is FA.
- The stress at any cross section is 2FA.
- The total extension is 3FLAY.
- The total elongation is 6FLAY.