Practice questions on Thermal Expansion and Thermal stress

Question 1
A pendulum clock gives correct time at 20°C at a place where g=9.8m/ s2. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where of = 9.788m/s2. At what temperature will it give correct time? Coefficient of linear expansion of steel = 12X10-6°C-1.

Question 2
A metal rod 30.0 cm long expands by 0.075 cm when its temperature is raised from 0°C to 100°C.A rod of a different metal and of same length expands by 0.045 cm for the same raise in temperature. A third rod also 30.0 cm long is made up of the pieces of each of the above metals placed and to end. and expends 0.065 cm between 0°C and 100°C. Find the length of each portion of the composite bar.

Question 3
Suppose that a steel hoop could be constructed around the earth's equator, just fitting it at a temperature 20°C. What would be the thickness of space between hoop and the earth if the temperature of the hoop were increased by 1 °C.
αsteel = 1.2 × 10-5 °C-1

Question 4
Two brass rods and one steel rod of equal length L0 and equal cross-sectional are joined rigidly at their ends .All rods are in the state of zero tension at 0° C. Find the length of the system when the temperature is increased to θ.

Coefficient of linear expansion of steel=αs
Coefficient of linear expansion of brass=αb
Young modulus of steel=Ys
Young modulus of brass=Yb

Question 5 What will the length of steel and copper rod .So that length of steel rod is 5cm longer then the copper rod at all the temperature (αcopper=1.7X10-5 /C,αsteel=1.1X10-5 /C)

Question 6
A bimetallic strip is formed out of two identical strips .One of the copper and other of brass. The coefficient of linear expansion of the two metals are αc and αB.On heating the strip through the temperature change ΔT,the strip bends into an arc of the circle. Find the radius of the curvature of the strip

Question 7
Show that the moment of inertia of the solid body of any shape changes with the temperature as I=I0(1+2αθ) .Where I0 is the moment of inertia at 0° C and α coefficient of linear expansion of the solid

Question 8
A bimetallic strip is made of aluminium and steel ($\alpha _{Al} > \alpha _{Steel}$) on heating, the strip will
(a) remain straight
(b) get twisted
(c) will bend with aluminium on concave side
(d) will bend with steel on concave side.

Question 9
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly
(a) its speed of rotation increases.
(b) its speed of rotation decreases.
(c) its speed of rotation remains same.
(d) its speed increases because its moment of inertia increases

Question 10
Two rods one of aluminium and other made of steel having initial length $L_1$ and $L_2$ are connected together to form a single rod of length $L_1 + L_2$ . The coefficient of linear expansion for aluminium and steel are $\alpha _a$ and $\alpha _S$ respectively. If the length of each road increases by the same amount when their temperature are raised by T degree Celsius, the what is the ratio between $ \frac {L_1}{L_1 + L_2}$ ?
a.$ \frac {\alpha _s}{\alpha _a}$
b.$ \frac {\alpha _a}{\alpha _s}$
c.$ \frac {\alpha _s}{\alpha _a + \alpha _s}$
d.$ \frac {\alpha _a}{\alpha _a + \alpha _s}$

Question 11
A pendulum clock loses 12s a day if the temperature is 40 °C and gains 4s a day if the temperature is 20°C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion ($\alpha$) of the metal of the pendulum shaft are respectively :
(a)25°C ; $\alpha =1.85 \times 10^{-5} $/°C
(b)60°C ;$\alpha =1.85 \times 10^{-4}$ /°C
(c)30°C ;$\alpha=1.85 \times 10^{-3}$/°C
(d)55°C ;$\alpha=1.85 \times 10^{-2}$/°C

Question 12
A cubical block is floating inside a bath. The temperature of system is increased by small temperature $\Delta T$. It was found that the depth of submerged portion of cube does not change. Find the relation between coefficient of linear expansion ($\alpha$) of the cube and volume expansion of liquid ($\gamma$).
a. $\gamma =2\alpha$
b. $\gamma =\alpha$
c. $\gamma =3\alpha$
d. $\gamma =\frac {1}{2} \alpha$

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