When a block of iron floats in Hg at $0°C$, a fraction $K_1$ of its volumen= is submerged, while at temperature of $60°C$ a fraction $K_2$ is seen to be submersed. If the coefficient of volume expansion of iron is ${\gamma }_{Fe}$ and that of mercury is ${\gamma }_{Hg}$, 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. $\frac{1+60{\gamma }_{He}}{1-60{\gamma }_{Fe}}$

A pendulum clock runs faster by \(5\) s per day at \(20^{\circ}\mathrm {C}\) and goes slow by \(10\) s per day at \(35^{\circ}\mathrm {C}\). It shows the correct time at a temperature of:
1. \(27.5^{\circ}\mathrm {C}\)
2. \(25^{\circ}\mathrm {C}\)
3. \(30^{\circ}\mathrm {C}\)
4. \(33^{\circ}\mathrm {C}\)

The coefficients of linear expansion of brass and steel rods are \(\alpha_1\) and \(\alpha_2\), lengths of brass and steel rods are \(l_1\) and \(l_2\) respectively. If (\(l_2-l_1\)) is maintained the same at all temperatures, Which one of the following relations holds good?
1. \(\alpha_1 l_2^2=\alpha_2l_1^2\)
2. \(\alpha_1^2 l_2=\alpha_2^2l_1\)
3. \(\alpha_1 l_1=\alpha_2l_2\)
4. \(\alpha_1 l_2=\alpha_2l_1\)

The value of coefficient of volume expansion of glycerin is 5x10^-4 K^-1. The fractional change in the density of glycerin for a rise of 40°C in its temperature is -

1. 0.015
 

2. 0.020
 

3. 0.025
 

4. 0.010

To keep constant time, watches are fitted with balance wheel made of -

1. Invar                                 

2. Stainless steel

3. Tungsten                             

4. Platinum

The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume ? The volume elasticity of the cube is  $\beta$ and the coefficient of volume expansion is $\alpha$ -

1. $\frac{P}{\alpha \beta }$                                 

2. $\frac{P\alpha }{\beta }$

3. $\frac{P\beta }{\alpha }$                                 

4. $\frac{\alpha \beta }{P}$

The value of the coefficient of volume expansion of glycerine is \(5\times10^{-4}~\text{K}^{-1}.\) The fractional change in the density of glycerine for a rise of \(40^\circ \text{C}\) in its temperature is:$\mathrm{}$

A copper rod of \(88\) cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is:
\(\left(\alpha_{Cu}= 1.7\times10^{-5}~\text{K}^{-1}~\text{and}~\alpha_{Al}= 2.2\times10^{-5}~\text{K}^{-1}\right)\)

Two uniform rods of length \(L\) and \(2L\) and thermal coefficient of linear expansion \(2\alpha\)  and \(\alpha\) respectively, are connected as shown in the figure. The equivalent coefficient of linear expansion is: