Thermal Expansion

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A wooden wheel of radius $R$ is made of two semi-circular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area $S$ and length $L$ . $L$ is slightly less than $2 π R$ . To fit the ring on the wheel, it is heated so that its temperature rises by $Δ T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semi-circular parts together. If the coefficient of linear expansion of the metal is $α$ and its Young's modulus is $Y$ , the force that one part of the wheel applies on the other part is

2 π S Y α Δ T

(B)

S Y α Δ T

(C)

π S Y α Δ T

(D)

2 S Y α Δ T

JEE Main 2019

LEVELJEE Main

Two rods $A$ and $B$ of identical dimensions are at temperature $3 0^{\circ} C$ . If $A$ is heated upto $18 0^{\circ} C$ and $B$ upto $T^{\circ} C$ , then new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is $4 : 3$ , then the value of $T$ is

(A)

23 0^{\circ} C

(B)

27 0^{\circ} C

(C)

20 0^{\circ} C

(D)

25 0^{\circ} C

JEE Main 2020

LEVELJEE Main

When the temperature of a metal wire is increased from $0^{\circ} C$ to $1 0^{\circ} C$ , its length increases by $0.02%$ . The percentage change in its mass density will be closest to

An external pressure $p$ is applied on a cube at $0^{\circ} C$ so that it is equally compressed from all sides. $K$ is the bulk modulus of the material of the cube and $α$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by

(A)

\frac{p}{α K}

(B)

\frac{3 α}{p K}

(C)

3 p K α

(D)

\frac{p}{3 α K}

JEE Main 2021

LEVELJEE Main

A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will

(A)

bend towards the right

(B)

not bend but shrink

(C)

Neither bend nor shrink

(D)

bend towards the left

JEE Main 2020

LEVELJEE Main

Two different wires having lengths $L_{1}$ and $L_{2}$ and respective temperature coefficients of linear expansion $α_{1}$ and $α_{2}$ , are joined end-to-end. Then the effective temperature coefficient of linear expansion is

(A)

\frac{α _{1} L _{1} + α _{2} L _{2}}{L _{1} + L _{2}}

(B)

2 α_{1} α_{2}

(C)

\frac{α _{1} + α _{2}}{2}

(D)

4 \frac{α _{1} α _{2}}{α _{1} + α _{2}} \frac{L _{2} L _{1}}{( L _{1} + L _{2} ) ^{2}}

JEE Main 2020

LEVELJEE Main

A bakelite beaker has volume capacity of $500 cc$ at $3 0^{\circ} C$ . When it is partially filled with $V_{m}$ volume (at $3 0^{\circ} C$ ) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If $γ_{(beaker)} = 6 \times 1 0^{- 6}^{\circ} C^{- 1}$ and $γ_{(mercury)} = 1.5 \times 1 0^{- 4}^{\circ} C^{- 1}$ , where $γ$ is the coefficient of volume expansion, then $V_{m}$ (in cc) is close to ........... .

JEE Main 2019

LEVELJEE Main

A thermometer graduated according to a linear scale reads a value $x_{0}$ , when in contact with boiling water and $x_{0} /3$ , when in contact with ice. What is the temperature of an object in $^{\circ} C$ , if this thermometer in the contact with the object reads $x_{0} /2$ ?

Each side of a box made of metal sheet in cubic shape is $a$ at room temperature $T$ , the coefficient of linear expansion of the metal sheet is $α$ . The metal sheet is heated uniformly, by a small temperature $Δ T$ , so that its new temperature is $T + Δ T$ . Calculate the increase in the volume of the metal box.

(A)

4 π a^{3} α Δ T

(B)

4 a^{3} α Δ T

(C)

\frac{4}{3} π a^{3} α Δ T

(D)

3 a^{3} α Δ T

JEE Main 2020

LEVELJEE Main

A non-isotropic solid metal cube has coefficients of linear expansion as : $5 \times 1 0^{- 5} /^{\circ} C$ along the X-axis and $5 \times 1 0^{- 6} /^{\circ} C$ along the Y and the Z-axis. If the coefficient of volume expansion of the solid is $C \times 1 0^{- 6} /^{\circ} C$ , then the value of $C$ is …… .

JEE Main 2014

LEVELJEE Main

The pressure that has to be applied to the ends of a steel wire of length $10 cm$ to keep its length constant when its temperature is raised by $10 0^{\circ} C$ is (For steel, Young's modulus is $2 \times 1 0^{11} Nm^{- 2}$ and coefficient of thermal expansion is $1.1 \times 1 0^{- 5} K^{- 1}$ )

(A)

2.2 \times 1 0^{8} Pa

(B)

2.2 \times 1 0^{9} Pa

(C)

2.2 \times 1 0^{7} Pa

(D)

2.2 \times 1 0^{6} Pa

JEE Main 2021, 22 July Shift-II

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The area of cross-section of a railway track is $0.01 m^{2}$ . The temperature variation is $1 0^{\circ} C$ . Coefficient of linear expansion of material of track is $1 0^{- 5} /^{\circ} C$ . The energy stored per metre in the track is ...... $J/m$ . (Take, Young's modulus of material of track is $1 0^{11} Nm^{- 2}$ )

JEE Main 2021, 25 Feb Shift-I

LEVELJEE Main

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion (A) When a rod lying freely is heated, no thermal stress is developed in it. Reason (R) On heating, the length of the rod increases. In the light of the above statements, choose the correct answer from the options given below

(A)

Both A and R are true but R is not the correct explanation of A.

(B)

A is false but R is true.

(C)

A is true but R is false.

(D)

Both A and R are true and R is the correct explanation of A.

LEVELJEE Main

A metal rod of Young's modulus $Y$ and coefficient of thermal expansion $α$ is held at its two ends such that its length remains invariant. If its temperature is raised by $t^{\circ} C$ , the linear stress developed in it is

(A)

\frac{α t}{Y}

(B)

\frac{Y}{α t}

(C)

Y α t

(D)

\frac{1}{Y α t}

JEE Main 2021, 1 Sep Shift-II

LEVELJEE Main

A steel rod with $Y = 2.0 \times 1 0^{11} Nm^{- 2}$ and $α = 1 0^{- 5}^{\circ} C^{- 1}$ of length $4 m$ and area of cross-section $10 cm^{2}$ is heated from $0^{\circ} C$ to $40 0^{\circ} C$ without being allowed to extend. The tension produced in the rod is $x \times 1 0^{5} N$ , where the value of $x$ is ............. .

JEE Main 2019

LEVELJEE Main

A rod of length $L$ at room temperature and uniform area of cross-section $A$ , is made of a metal having coefficient of linear expansion $α /^{\circ} C$ . It is observed that an external compressive force $F$ , is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by $Δ T$ K. Young's modulus, $Y$ for this metal is

(A)

\frac{F}{2 A α Δ T}

(B)

\frac{F}{A α ( Δ T - 273 )}

(C)

\frac{2 F}{A α Δ T}

(D)

\frac{F}{A α Δ T}

JEE Advanced (2004)

LEVELJEE Advanced

A cube of coefficient of linear expansion $α_{s}$ is floating in a bath containing a liquid of coefficient of volume expansion $γ_{l}$ . When the temperature is raised by $Δ T$ , the depth upto which the cube is submerged in the liquid remains the same. Find the relation between $α_{s}$ and $γ_{l}$ showing all the steps.

JEE Advanced 2011

LEVELJEE Main

Steel wire of length $L$ at $4 0^{\circ} C$ is suspended from the ceiling and then a mass $m$ is hung from its free end. The wire is cooled down from $4 0^{\circ} C$ to $3 0^{\circ} C$ to regain its original length $L$ . The coefficient of linear thermal expansion of the steel is $1 0^{- 5} /^{\circ} C$ , Young's modulus of steel is $1 0^{11} N/m^{2}$ and radius of the wire is $1 mm$ . Assume that $L ≫ diameter of the wire$ . Then the value of $m$ in kg is nearly.

LEVELJEE Advanced

The apparatus shown in figure consists of four glass columns connected by horizontal sections. The height of two central columns $B$ and $C$ are $49 cm$ each. The two outer columns $A$ and $D$ are open to the atmosphere. $A$ and $C$ are maintained at a temperature of $9 5^{\circ} C$ while the columns $B$ and $D$ are maintained at $5^{\circ} C$ . The height of the liquid in $A$ and $D$ measured from the base line are $52.8 cm$ and $51 cm$ respectively. Determine the linear coefficient of thermal expansion of the liquid.

JEE Advanced 1999

LEVELJEE Advanced

A bimetallic strip is formed out of two identical strips– one of copper and the other of brass. The coefficients of linear expansion of the two metals are $α_{C}$ and $α_{B}$ . On heating, the temperature of the strip goes up by $Δ T$ and the strip bends to form an arc of radius of curvature $R$ . Then, $R$ is

* Multiple Correct Options

(A)

proportional to

Δ T

(B)

inversely proportional to

Δ T

(C)

proportional to

∣ α_{B} - α_{C} ∣

(D)

inversely proportional to

∣ α_{B} - α_{C} ∣

JEE Advanced 2007

LEVELJEE Main

Column I gives some devices and Column II gives some processes on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II.

List-I

List-II

(1)

Radiation from a hot body

Thermal expansion of solids

LEVELJEE Advanced

A composite rod is made by joining a copper rod, end to end, with a second rod of different material but of the same cross-section. At 25°C, the composite rod is 1 m in length, of which the length of the copper rod is 30 cm. At 125°C the length of the composite rod increases by 1.91 mm. When the composite rod is not allowed to expand by holding it between two rigid walls, it is found that the length of the two constituents do not change with the rise of temperature. Find the Young's modulus and the coefficient of linear expansion of the second rod. (Given, Coefficient of linear expansion of copper = $1.7 \times 1 0^{- 5} per^{\circ} C$ , Young's modulus of copper = $1.3 \times 1 0^{11} N/m^{2}$ )

LEVELJEE Advanced

A sinker of weight $w_{0}$ has an apparent weight $w_{1}$ when placed in a liquid at a temperature $T_{1}$ and $w_{2}$ when weighed in the same liquid at a temperature $T_{2}$ . The coefficient of cubical expansion of the material of the sinker is $β$ . What is the coefficient of volume expansion of the liquid ?

JEE Advanced 2001

LEVELJEE Main

When a block of iron floats in mercury at $0^{\circ} C$ , fraction $k_{1}$ of its volume is submerged, while at the temperature $6 0^{\circ} C$ , a fraction $k_{2}$ is seen to be submerged. If the coefficient of volume expansion of iron is $γ_{Fe}$ and that of mercury is $γ_{Hg}$ , then the ratio $k_{1} / k_{2}$ can be expressed as

(A)

\frac{1 + 60 γ _{Fe}}{1 + 60 γ _{Hg}}

(B)

\frac{1 - 60 γ _{Fe}}{1 + 60 γ _{Hg}}

(C)

\frac{1 + 60 γ _{Fe}}{1 - 60 γ _{Hg}}

(D)

\frac{1 + 60 γ _{Hg}}{1 + 60 γ _{Fe}}

JEE Advanced 1991

LEVELJEE Main

A piece of metal floats on mercury. The coefficients of volume expansion of the metal and mercury are $γ_{1}$ and $γ_{2}$ respectively. If the temperatures of both mercury and the metal are increased by an amount $Δ T$ , the fraction of the volume of the metal submerged in mercury changes by the factor ......

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } When the temperature of a metal wire is increased from 0∘C to 10∘C, its length increases by 0.02%. The percentage change in its mass density will be closest to

A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will

Column I gives some devices and Column II gives some processes on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II.

List-I

List-II

When the temperature of a metal wire is increased from $0^{\circ} C$ to $1 0^{\circ} C$ , its length increases by $0.02%$ . The percentage change in its mass density will be closest to