Thermal Expansion

Q.

If the earth were to suddenly contract to 1/n^th of its present radius without any change in its mass, the duration of the new day will be nearly

1. 24/n hr

2. 24nhr

3. 24/n²hr

4. 24n²hr

Q.

Find the expression for the time period of a pendulum using dimensional analysis.

1. $k\sqrt{\frac{g}{l}}$

2. kl

3. $k\sqrt{\frac{l}{g}}$

4. $\frac{kl}{g}$

Q.

When two ends of a rod wrapped with cotton are maintained at different temperatures and after some time every point of the rod attains a constant temperature, then

1. Conduction of heat at different points of the rod stops because the temperature is not increasing

2. Rod is bad conductor of heat

3. Heat is being radiated from each point of the rod

4. Each point of the rod is giving heat to its neighbour at the same rate at which it is receiving heat

Q.

Solids expand on heating because

1. Kinetic energy of the atoms increases

2. Potential energy of the atoms increases

3. Total energy of the atoms increases

4. The potential energy curve is asymmetric about the equilibrium distance between neighbouring atoms

Q. A hole is drilled in a copper sheet. The diameter of the hole is $4.24\text{cm}$ at $27{}^{\circ }\text{C}$. What is the change in the diameter of the hole when the sheet is heated to $227{}^{\circ }\text{C}$ ?
$[\alpha =1.70\times {10}^{-5}/{}^{\circ }\text{C}]$.

1. $1.44\times {10}^{-2}\text{cm}$
2. $1.96\times {10}^{-2}\text{cm}$
3. $1.78\times {10}^{-2}\text{cm}$
4. $1.28\times {10}^{-2}\text{cm}$

Q. The system shown in the figure consists of three springs and two rods of the same material as shown in the figure. The springs are initially relaxed and there is no friction. The temperature of the rods is increased by $\Delta T$. The coefficient of linear expansion of the material of the rods is $\alpha$. Then, energy stored in the spring $1$, when the system is in equilibrium, is:

1. $\frac{75}{242}k{L}^2{\alpha }^2(\Delta T{)}^2$
2. $\frac{27}{242}k{L}^2{\alpha }^2(\Delta T{)}^2$
3. $\frac{81}{242}k{L}^2{\alpha }^2(\Delta T{)}^2$
4. $\frac{49}{242}k{L}^2{\alpha }^2(\Delta T{)}^2$

Q. A scale which is calibrated at ${10}^{\circ }\text{C}$ measures the length of a stick to be $60\text{cm}$, at temperature ${30}^{\circ }\text{C}$ . If thermal coefficient of linear expansion of the rod is $2\times {10}^{-5}{/}^{\circ }\text{C}$, the correct length of the stick in $\text{cm}$ is:

1. $60.015$
2. $60.024$
3. $60.400$
4. $60.600$

Q.

The Unit of Coefficient of Linear Expansion is _______

Q. A composite rod is made of copper $\alpha =1.8\times {10}^{-5}{K}^{-1}$ and steel $1.2\times {10}^{-5}{K}^{-1}$ as shown in figure, is heated up, then it

1. $\text{bends with steel on concave side}$
2. $\text{bends with copper on concave side}$
3. $\text{dose not expand}$
4. $\text{data is insufficient}$

Q. A bimetallic strip on heating has radius $R$. The coefficients of thermal expansion are ${\alpha }_1$ and ${\alpha }_2$. If the strip having greater coefficient of thermal expansion $\left({\alpha }_1\right)$ is replaced by an identical strip having coefficient of thermal expansion $3$ times its value (i.e $3{\alpha }_1$) and heated to the same temperature difference, then the new radius of the arc is
[ given, $\frac{{\alpha }_1}{{\alpha }_2}=2$ ]

1. $\frac{R}{5}$
2. $2R$
3. $5R$
4. $\frac{R}{2}$

Q. Two rods of different materials having coefficients of thermal expansion ${\alpha }_1,{\alpha }_2$ and Young's modulii $Y_1,Y_2$ 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 ${\alpha }_1:{\alpha }_2=2:3$ and thermal stresses developed in the two rods are equal, then $Y_1:Y_2$ is equal to

1. $2:3$
2. $1:1$
3. $3:2$
4. $4:9$

Q. Temperature of a bimetallic strip of copper and zinc rivetted together is increased from ${20}^{\circ }\text{C}$ to ${100}^{\circ }\text{C}$. Which of the following options correctly represents the final condition of the bimetallic strip?
$[Z{n}_{\alpha }=30\times {10}^{-6}/{}^{\circ }C,C{u}_{\alpha }=17\times {10}^{-6}/{}^{\circ }C]$

1. Zinc strip will be on outer side of arc.
2. Copper strip will be on outer side of arc.
3. Bimetal will not bend.
4. Data insufficient

Q.

Identify the device shown in figure.

Q.

A cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap as shown. On heating the system -

1. $x$ decreases, $r$ and $d$ increase

2. $x$ and $r$ increase, $d$ decreases

3. $x$, $r$ and $d$ all increase

4. Data insufficient to arrive at a conclusion

Q.

A litre of alcohol weighs

1. Less in winter than in summer

2. Less in summer than in winter

3. Some both in summer and winter

4. None of the above

Q. A sphere of mass $M$ and diameter $D$ is heated by temperature $\Delta T$. If coefficient of linear expansion is $\alpha$, then find the change in the surface area of sphere.

1. $\pi D^2\alpha \Delta T(\alpha \Delta T+2)$
2. $\pi D^2\alpha \Delta T(\alpha \Delta T-2)$
3. $\pi D^2\alpha \Delta T(\alpha \Delta T+4)$
4. $\pi D^2\alpha \Delta T(\alpha \Delta T-4)$

Q. When the temperature of a rod increases from $t$ to $t+\Delta t$, its moment of inertia about a perpendicular axis passing through its centre increases from $I$ to $I+\Delta I$. If $\alpha$ be the coefficient of linear expansion of the rod, then the value of $\frac{\Delta I}{I}$ is

1. $2\alpha \Delta t$
2. $\alpha \Delta t$
3. $3\alpha \Delta t$
4. $4\alpha \Delta t$

Q. A seconds pendulum clock has a steel wire. The clock shows correct time at ${25}^{\circ }\text{C}$. How much time does the clock lose or gain in one week, when the temperature is increased to ${35}^{\circ }\text{C}$ ? $({\alpha }_{steel}=1.2\times {10}^{-5}{/}^{\circ }\text{C})$

1. $5.18\text{s}$ gain
2. $5.18\text{s}$ lose
3. $36.28\text{s}$ gain
4. $36.28\text{s}$ lose

Q. A seconds pendulum clock has a steel wire. The clock shows correct time at ${25}^{\circ }\text{C}$. How much time does the clock lose or gain in one week, when the temperature is increased to ${35}^{\circ }\text{C}$ ? $({\alpha }_{steel}=1.2\times {10}^{-5}{/}^{\circ }\text{C})$

1. $5.18\text{s}$ gain
2. $5.18\text{s}$ lose
3. $36.28\text{s}$ gain
4. $36.28\text{s}$ lose

Q. A pendulum clock consists of an iron rod connected to a small, heavy bob. If it is designed to keep correct time at ${20}^{\circ }C$, how fast or slow will it go in 24 hours at ${40}^{\circ }C$? Coefficient of linear expansion of iron = $1.2\times {10}^{-5}{/}^{\circ }C$.

1. 10.4 seconds faster
2. 10.4 minutes faster
3. 1 minute slower
4. 10.4 seconds slower

Q. Two rods of different materials and of equal cross-sectional areas and length $1\text{m}$ 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 $30{}^{\circ }\text{C}$, the magnitude of the displacement of the joint of the rods is :
$[{\alpha }_1=2\times {10}^{-5}{}^{\circ }{\text{C}}^{-1},{\alpha }_2=5\times {10}^{-5}{}^{\circ }{\text{C}}^{-1},$
$Y_1=2\times {10}^{10}{\text{N/m}}^2,Y_2={10}^{10}{\text{N/m}}^2]$

1. $15\times {10}^{-5}\text{m}$
2. $12\times {10}^{-5}\text{m}$
3. $10\times {10}^{-5}\text{m}$
4. $18\times {10}^{-5}\text{m}$

Q.

When a bimetallic strip is heated, it

1. Does not bend at all

2. Gets twisted in the form of an helix

3. Bend in the form of an arc with the more expandable metal outside

4. Bends in the form of an arc with the more expandable metal inside

Q. A sphere of mass $M$ and diameter $D$ is heated by temperature $\Delta T$. If coefficient of linear expansion is $\alpha$, then find the change in the surface area of sphere.

1. $\pi D^2\alpha \Delta T(\alpha \Delta T+2)$
2. $\pi D^2\alpha \Delta T(\alpha \Delta T-2)$
3. $\pi D^2\alpha \Delta T(\alpha \Delta T+4)$
4. $\pi D^2\alpha \Delta T(\alpha \Delta T-4)$

Q. A hole is drilled in a copper sheet. The diameter of the hole is $4.24\text{cm}$ at $27{}^{\circ }\text{C}$. What is the change in the diameter of the hole when the sheet is heated to $227{}^{\circ }\text{C}$ ?
$[\alpha =1.70\times {10}^{-5}/{}^{\circ }\text{C}]$.

1. $1.44\times {10}^{-2}\text{cm}$
2. $1.96\times {10}^{-2}\text{cm}$
3. $1.78\times {10}^{-2}\text{cm}$
4. $1.28\times {10}^{-2}\text{cm}$

Q. A tape measures the length of a copper rod as $90\text{cm}$ at ${10}^{\circ }C$. What would the tape read for the length of the rod at ${30}^{\circ }C$?
Given, ${\alpha }_{\text{Cu}}=1.7\times {{10}^{-5}}^{\circ }{C}^{-1}$

1. $90\text{cm}$
2. $90.01\text{cm}$
3. $90.3\text{cm}$
4. $90.03\text{cm}$

Q. A clock with a metal pendulum beating seconds keeps correct time at $0^{\circ }C.$ If it loses 12.5 seconds a day at ${25}^{\circ }C,$ the coefficient of linear expansion of metal of pendulum is

1. $\frac{1}{86400}pe{r}^{\circ }C$
2. $\frac{1}{43200}pe{r}^{\circ }C$
3. $\frac{1}{14400}pe{r}^{\circ }C$
4. $\frac{1}{28800}pe{r}^{\circ }C$

Q. The coefficient of linear expansion of brass and steel are
${\alpha }_1$ and ${\alpha }_2$. If we take a brass rod of length $l_1$ and steel rod of length $l_{2}at{0}^{\circ }C,$ their difference in length $(l_2-l_1)$will remain the same at a temperature if

1. ${\alpha }_1{l}_2={\alpha }_2{l}_1$
2. ${\alpha }_1{l}_2^2={\alpha }_2{l}_1^2$
3. ${\alpha }_1^2{l}_1={\alpha }_2^2{l}_2$
4. ${\alpha }_1{l}_1={\alpha }_2{l}_2$

Q.

A pendulum clock keeps correct time at $0^{\circ }$. Its mean coefficient of linear expansions is $\alpha {/}^{\circ }$, then the loss in seconds per day by the clock if the temperature rises by $t^{\circ }$ is

1. $\frac{\frac{1}{2}\alpha t\times 864000}{1-\frac{\alpha t}{2}}$

2. $\frac{1}{2}\alpha t\times 86400$

3. $\frac{\frac{1}{2}\alpha t\times 86400}{{(1-\frac{\alpha t}{2})}^2}$

4. $\frac{\frac{1}{2}\alpha t\times 846400}{1+\frac{\alpha t}{2}}$

Q. The coefficient of linear expansion of steel and brass are $11\times {10}^{-6}{/}^{\circ }\text{C}$ and $19\times {10}^{-6}{/}^{\circ }\text{C}$, respectively. If their differences in lengths at all temperatures has to kept constant at $30\text{cm}$, their lengths at $0^{\circ }\text{C}$ should be

1. $71.25\text{cm}$ and $41.25\text{cm}$
2. $82\text{cm}$ and $52\text{cm}$
3. $92\text{cm}$ and $62\text{cm}$
4. $62.25\text{cm}$ and $32.25\text{cm}$

Q. An aluminium measuring rod, which is correct at $5^{\circ }\text{C}$ measures the length of a line as $80\text{cm}$ at ${45}^{\circ }\text{C}$. If thermal coefficient of linear expansion of aluminium is $2.50\times {10}^{-5}{/}^{\circ }\text{C}$, the correct length of the line is

1. $80.08\text{cm}$
2. $79.92\text{cm}$
3. $81.12\text{cm}$
4. $79.62\text{cm}$