Area and Volume Expansion

Q.

A vertical column 50 cm long at ${50}^{c}irc$ C balances another column of same liquid 60 cm long at ${100}^{c}irc$°C. The coefficient of absolute expansion of the liquid is

1. 0.005/°C

2. 0.0005/°C

3. 0.002/°C

4. 0.0002/°C

Q.

A non-isotropic solid metal cube has coefficient of linear expansion as $5\times {10}^{-5}/{}^{0}C$ along the x-axis and$5\times {10}^{-6}/{}^{0}C$ along y-axis and z-axis. If the coefficient of volumetric expansion of the solid is $C\times {10}^{-6}/{}^{0}C$then the value of $C$ is.

Q. The coefficient of volume expansion of glycerine is 49 × 10¯⁵ K¯¹. What is the fractional change in its density for a 30 °C rise in temperature ?

Q. On heating a uniform metallic cylinder, length increases by $3\%$. The area of cross - section of its base will increase by

1. $1.5\%$
2. $3\%$
3. $9\%$
4. $6\%$

Q.

A glass flask is filled up to a mark with 50 cc of mercury at ${18}^{\circ }C$ . If the flask and contents are heated to ${38}^{\circ }C$ , how much mercury will be above the mark ? ( for glass is 9 × ${10}^{-6}{/}^{\circ }C$ and coefficient of real expansion of mercury is 180 × ${10}^{-6}{/}^{\circ }C$)

1. 0.46 cc

2. 0.85 cc

3. 0.05 cc

4. 0.153 cc

Q. Two cylinders of same cross section and length L but made of two materials of density ρ1 and ρ2 are cemented together to form a cylinder 2L. If the combination floats in water with length L/2 above the surface of water ρ1<ρ2, then A. ρ1>1g/cc B. ρ1<8/9 g/cc C. ρ1>3/2 g/cc D. ρ1<3/4 g/c

Q. An annular disc of inner radius $a$ and outer radius $2a$ is uniformly charged with uniform surface charge density $\sigma$. Find the potential at a distance $a$ from the centre at a point $P$ lying on the axis which is perpendicular to the plane containing the disc.

1. $$\frac{\sigma }{2{ϵ}_0}a$$
   
2. $\frac{\sigma }{{ϵ}_0}a(\sqrt{5}-\sqrt{2})$
   
3. $\frac{\sigma }{2{ϵ}_0}a(\sqrt{5}-\sqrt{2})$
4. $\frac{\sigma }{2{ϵ}_0}(\sqrt{3}-\sqrt{2})$
   

Q. A glass flask of volume one litre at $0{}^{\circ }\text{C}$ is filled, level full of mercury at this temperature. The flask and mercury are now heated to $100{}^{\circ }\text{C}$. Find the amount of mercury that will spill out, if the coefficient of volume expansion of mercury is $1.82\times {10}^{-4}{/}^{\circ }\text{C}$ and the coefficient of linear expansion of glass is $0.1\times {10}^{-4}{/}^{\circ }\text{C}$ respectively.

1. $21.2\text{cc}$
2. $15.2\text{cc}$
3. $1.52\text{cc}$
4. $2.12\text{cc}$

Q.

On a hot day in Jaipur, an oil trucker loaded 40 kL (kilolitres) of diesel fuel. On his way to Shimla, he encounters a temperature drop of ${20}^{\circ }C$, where he stopped and delivered the entire load. How many litres did he deliver? The γ for diesel is $9.50\times {10}^{-4}{/}^{\circ }C$ and α for his steel truck is $11\times {10}^{-6}{/}^{\circ }C$. If you find that the volume has decreased, think about who is paying for the "missing” diesel.

1. 39, 810 L

2. 40, 000 L

3. 39, 240 L

4. 40, 126 L

Q. 41.Two slabs A and B of different materials but of the same thickness are joined end to end to form a composite slab.Thermal conductivities of A and B are K1 and K2 are respectively.A steady temperature difference of 12 degree celcious is maintained across the composite slab.If K1=K2/2 the temperature difference across the slab A is

Q. The coefficient of volume expansion of a liquid is $5\times {10}^{-4}{{}^{\circ }\text{C}}^{-1}$. If its temperature is increased by ${30}^{\circ }\text{C}$, the percentage change in its density is

Q.

The coefficient of apparent expansion of mercury in a glass vessel is 153 × ${10}^{-6}{/}^{\circ }C$ and in a steel vessel is 144 × ${10}^{-6}{/}^{\circ }C$. If afor steel is 12 × ${10}^{-6}{/}^{\circ }C$, then that of glass is

1. $9\times {10}^{-6}{/}^{\circ }C$

2. $6\times {10}^{-6}{/}^{\circ }C$

3. $36\times {10}^{-6}{/}^{\circ }C$

4. $27\times {10}^{-6}{/}^{\circ }C$

Q. The coefficient of linear expansion of a crystalline substance in one direction is $2\times {10}^{-4}{/}^{\circ }\text{C}$ and in every direction perpendicular to it is $3\times {10}^{-4}{/}^{\circ }\text{C}$. The coefficient of cubical expansion of the crystal is equal to

1. $5\times {10}^{-4}{/}^{\circ }\text{C}$
2. $4\times {10}^{-4}{/}^{\circ }\text{C}$
3. $8\times {10}^{-4}{/}^{\circ }\text{C}$
4. $7\times {10}^{-4}{/}^{\circ }\text{C}$

Q. An aluminium sphere of $20\text{cm}$ diameter is heated from $0^{\circ }C$ to ${100}^{\circ }C$. Its volume changes by (given that coefficient of linear expansion for aluminium ${\alpha }_{Al}=23\times {10}^{-6}{/}^{\circ }C$

1. $28.9\text{cc}$
2. $2.89\text{cc}$
3. $9.28\text{cc}$
4. $49.8\text{cc}$

Q. A glass bulb of volume $250cc$ is filled with mercury at ${20}^{o}C$ and the temperature is raised to ${100}^{o}C$. If the coefficient of linear expansion of glass is $9\times {10}^{-6}{/}^{o}C$. Coefficient of absolute expansion of mercury is $18\times {10}^{-5}{/}^{o}C$. The volume of mercury overflows

1. $3.06cc$
2. $2.94cc$
3. $6.12cc$
4. $7.73cc$

Q. A one litre glass flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume of mercury in this flask if coefficient of linear expansion of glass is $9\times {10}^{-6}{/}^{\circ }C$ while of volume expansion of mercury is $1.8\times {10}^{-4}{/}^{\circ }C$

Q.

A piece of metal floats in mercury. The coefficients of volume expansion of the metal and mercury are ${\gamma }_1$ and ${\gamma }_2$ respectively. If their temperature is increased by $\Delta T$, the fraction of the volume of metal submerged in mercury changes by a factor

1. $\left(\frac{1+{\gamma }_2\Delta T}{1+{\gamma }_1\Delta T}\right)$

2. $\left(\frac{1+{\gamma }_2\Delta T}{1-{\gamma }_1\Delta T}\right)$

3. $\left(\frac{1-{\gamma }_2\Delta T}{1+\gamma \Delta T}\right)$

4. $\frac{{\gamma }_2}{{\gamma }_1}$

Q.

A sphere and a cube of same material and same volume are heated up to same temperature and allowed to cool in the same surroundings. The ratio of the amounts of radiations emitted in equal time1 intervals will be

1. 

2. 

3. 

4. 

Q. Liquid is filled in a flask upto a certain point. When, the flask is heated, the level of the liquid :

1. initially falls and then rises
2. immediately starts increasing
3. falls abruptly
4. rises abruptly

Q. (A): the linear expansion of metal wire is $1$% when it is heated from $T_1$to $T_2$ (in ${}^{o}C$). id a thin plat of same metal of dimension $2L\times L$ was heated from $T_1$ to $T_2$, then the areal expansion is $3$%.

1. A and B are correct and B is correct explanation for A
2. A and B are correct and B is not correct explanation for A
3. A is true and B is false
4. A is wrong and B is true.

Q. A mercury-in-glass thermometer has a stem of internal diameter 0.06 cm and contains 43 g of mercury. The mercury thread expands by 10 cm when the temperature changes from $0^{\circ }C$ to ${50}^{\circ }C$. Find the coefficient of cubical expansion of mercury. Relative density of mercury = 13.6 and ${\alpha }_{glass}=9\times {10}^{-6}{K}^{-1}$

1. ${10}^{-5}{K}^{-1}$
2. $2\times {10}^{-5}{K}^{-1}$
3. $10.7\times {10}^{-5}{K}^{-1}$
4. $20.7\times {10}^{-5}{K}^{-1}$

Q. A glass flask of volume one litre is filled completely with mercury at $0^{o}C$. The flask is now heated to ${100}^{o}C$. Coefficient of volume expansion of mercury is $1.82\times {10}^{-4}{/}^{o}C$ and coefficient of linear expansion of glass is $0.1\times {10}^{-4}{/}^{o}C$. During this process, amount of mercury which overflows is :

1. 15.2 cc
2. 21.2 cc
3. 2.12 cc
4. 18.2 cc

Q. in stress strain curve where we have to locate elastomers on fracture point or at point D or at between point D and E

Q.

A gas in an airtight container is heated from ${25}^{\circ }C$ to ${90}^{\circ }C$. The density of the gas will:
( Consider there is a negligible expansion of container)

1. Increase slightly

2. Increase considerably

3. Remain the same

4. Decrease slightly

Q. A crystal has a coefficient of expansion 13 x ${10}^{-7}$ $12\times {10}^{-7}{/}^{0}C$ and $10\times {10}^{-7}{/}^{0}C$ in three mutually perpendicular directions respectively$.$ Then the coefficient of cubical expansion of the crystal is

1. 46 x ${10}^{-7}$
2. 24 x ${10}^{-7}$
3. 35x ${10}^{-7}$
4. 25 x ${10}^{-7}$

Q. Thermal coefficient of volume expansion at constant pressure for an ideal gas sample of $n$ moles having pressure $P_o$, volume $V_o$ and temperature $T_o$ is:

1. $\frac{R}{P_o{V}_o}$
2. $\frac{P_o{V}_o}{R}$
3. $\frac{1}{T_o}$
4. $\frac{1}{n{T}_o}$

Q. An insulated chamber at a height $h$ above the earth’s surface and maintained at ${30}^{\circ }C$ has a clock fitted with an uncompensated pendulum. The maker of the clock for the chamber mistakenly designs it to maintain correct time at ${20}^{\circ }C$ at that height. It is found that if the chamber were brought to earth’s surface the clock in it would click correct time at ${30}^{\circ }C$. The coefficient of linear expansion of the material of pendulum is (earth’s radius is $R$):

1. $\frac{R}{5h}$
2. $\frac{5R}{h}$
3. $\frac{h}{5R}$
4. $\frac{h}{20R}$

Q. When a block of iron floats in mercury at $0^{\circ }C$, a fraction $k_1$ of its volume submerged, while at the temperature ${60}^{\circ }C$, a fraction $k_2$ is keen to be submerged the coefficient of volume expansion of iron of $g_{Fe}$ and that of mercury is $g_{Hg}$, then the ratio $\frac{k_1}{k_2}$ can be expressed as

1. $\frac{1+60{\gamma }_{Fe}}{1+60{\gamma }_{Hg}}$
2. $\frac{1-60{\gamma }_{Fe}}{1+60{\gamma }_{Hg}}$
3. $\frac{1+60{\gamma }_{Fe}}{1-60{\gamma }_{Hg}}$
4. $\frac{1+60{\gamma }_{Hg}}{1+60{\gamma }_{Fe}}$

Q.

5 litre of benzene weighs

1. More in summer than in winter

2. More in winter than in summer

3. Equal in winter and summer

4. None of the above

Q. Identify the correct statements from the following

1. The apparent expansion of liquid depends on the expansion of material of the container
2. The real expansion of the liquid depends on the density of the liquid
3. The expansion of liquid with respect to the container is called the apparent expansion
4. The expansion of water is uniform