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1.	The linear expansivity of glass is `8xx10^(-6)K^(-1)` and cubical expansivity of mercury is `18xx10^(-5)K`. What volume of mercury must be placed inside a flask of 300cc, so that the volume of the flask not occupied by mercury may remain the same all temperature?
Answer» Correct Answer - 40cc

2.	A glass tube is attached to the bottom of a thin iron rod of length `1m`. To what height must the glass tube be filled with mercury so that the centre of mass of the pendulum formed will not rise or all with changes in temperature? (Linear expansivity of glass `=9xx10^(-6)K^(-1)`, that of iron `=12x10^(-6)K^(-1)` and cubical edxpansivity of mercury `=18.2xx10^(-5)K^(-1)`)
Answer» Correct Answer - `0.146m`

3.	The compensated pendulum of a clock consista of an isosceles triangular frame of base length `l_(1)` and expansivity `alpha_(1)` and side length `l_(2)` and expansivity `alpha_(2)`. The pendulum is supported as shown in the figure. Calculate the ratio `l_(1)//l_(2)` so that the length of the pendulum may remain unchanged at all temperatures?
Answer» Correct Answer - `(l_(1))/(l_(2))=2 sqrt((alpha_(2))/(alpha_(1)))`

4.	A glass hydrometer reads 9200 in a liquid at `45^(@)C`. What would be the reading at `15^(@)C`? (Cubical expansivity of the liquid `=52.xx10^(-5)//K` and that of glass `=2.4xx10^(-5)//K`)
Answer» Correct Answer - `0.9338`

5.	A bimetallic strip consiting of a brass strip and a steel strip, each of length `1m` and thickness `1//2` cm is clamped at one end at `0^(@)C`.Calculate the depression of the free end when it is heated to `100^(@)C`.
Answer» Correct Answer - `4cm`

6.	If a clock with an uncompensated pendulum of steel keeps correct time at `15^(@)C` how many seconds would it lose is 24 hours at a temperature of `25^(@)`? (Linear expansivity of steel `=12xx10^(-6)K^(-1)`)
Answer» Correct Answer - `5.2s`

7.	A vessel of volume `0.02m^(3)` contains a mixture of hydrogen and helium, at `20^(@)C` and 2 atm pressure. The mass of the mixture is equal to `5g`. Find the ratio of the mass of hydrogen to that of helium in the given mixture.
Answer» Correct Answer - 0.5

8.	An iron scale is correct at `0^(@)C` an at this temperature, a zinc rod measures `1m` on this scale. What will be the length of the zinc rod as measured by the iron scale when both the are at `100^(@)C`? (Linear expansivity of zinc `=126xx10^(-6)K^(-1)` and linear expansivity of iron `=12x10^(-6)K^(-1)`)
Answer» Correct Answer - `1.0014cm`

9.	The scale of a barometer is made of brass and is correct is `15^(@)C`. The reading of the barometer is `0.754m` at `5^(@)C`. Correct this reading to `0^(@)C`. (Linear expansivity of brass `=18x10^(-6)K^(-1)` and cubical expansivity of mercury `=18xx10^(-5)K^(-1)`)
Answer» Correct Answer - `0.7532m`

10.	A composite bar of length `L=L_(1)+L_(2)` is made from a bar of material 1 and length `L_(1)` attached to a bar of material 2 and length `L_(2)`. Find the effective linear expansion `alpha` of this bar.The coefficinets of linear expansion of the material of the rods are `alpha_(1)` and `alpha_(2)` respectively.
Answer» Correct Answer - `(alpha_(1)L_(1)+alpha_(2)+alpha_(2)L_(2))/(L_(1)+L_(2))`

11.	As a result of temperature rise of `32^(@)C` a bar with a crack at its centre buckles upwards. If the fixed distance be `L_(0)=4.0m` and the temperature coefficient of linear expansion be `alpha=25xx10^(-6)//C^(@)`, find the distance `x` by which the centre rises.
Answer» Correct Answer - `8cm`

12.	A sinker of weight `w_(0)` ha an apparent weight `w_(1)` when weighed in a liquid at temperature `t_(1)` and `w_(2)` when weighed in the same liquid at temperature `t_(2)`. The coefficient of cubical expansion of the material of the sinker is `beta`. What is the coefficient of volume expansion of the liquid?
Answer» Correct Answer - `(W_(0)-W_(1))/(W_(0)-W_(2))beta`

13.	Three equal -length straight rods, of aluminium invar and steel all at `20^(@)C`, form an equilateral triangle with hinge pins at the vertices. At what temperature will the angle opposite to the invar rod be `59.95^(@)`? `alpha_("invar")=0.7xx10^(-6)//C^(@), alpha_("steel")=11xx10^(-6)//C^(@), alpha_("aluminium")=23xx10^(-6)//C^(@)`
Answer» Correct Answer - `45.3^(@)C`

14.	A circular hole in an aluminium plate has a diameter of `4cm` at `0^(@)C`. What is its diameter when the temperature of the plate is raised to `100^(@)C`? (Linear expansivity of aluminium `=23xx10^(-6)K^(-1)`)
Answer» Correct Answer - `4.0092cm`

15.	A certain property `eta` varies according to the law `eta=(alpha(t-t_(0)))/(1+alphat)` where `alpha` is a constant and `t_(0)` is a temperature less than `t`. If `etagt1` is unthinkable what is the absolute zero on this property? What is the relation of `t` and `T` on this property?
Answer» Correct Answer - `T=T+1/(alpha)`