Water from a pipe is coming at a rate of \(100\text{ liters per minute}.\) If the radius of the pipe is \(5\text{ cm},\) the Reynolds number for the flow is of the order of- (density of water = \(1000\text{ kg/m}^3,\) coefficient of viscosity of water = \(1 \text{ mPa-s}\))
1. \(10^4\)${\mathrm{}}^{}$

2. \(10^3\)${\mathrm{}}^{}$

3. \(10^2\)${\mathrm{}}^{}$

4. \(10\)

If \(M\) is the mass of water that rises in a capillary tube of radius \(r,\) then mass of water which will rise in a capillary tube of radius \(2r\) is:
1. \(M\)
2. \(4M\)
3. \(M/2\)
4. \(2M\)

A hollow spherical shell of outer radius \(R\) floats just submerged beneath the surface of water. The inner radius of the shell is \(r.\) If the specific gravity of the shell material with respect to water is \(\dfrac{27}{8},\) what is the value of \(r\text{?}\)
\( \left (\text{use:}~19^{1/3}= \dfrac{8}{3}\right )\)

In an adiabatic process, the density of a diatomic gas becomes \(32\) times its initial value. The final pressure of the gas is found to be \(n\) times the initial pressure. The value of \(n\) is:
1. \(326\)
2. \(\dfrac{1}{32}\)
3. \(32\)
4. \(128\)

In an experiment to verify Stokes's law, a small spherical ball of radius \(r\) and density \(\rho\) falls under gravity through a distance \(h\) in air before entering a tank of water. If the terminal velocity of the ball inside water is the same as its velocity just before entering the water surface, then the value of \(h\) is proportional to: (Ignore viscosity of air)
1. \(r\)
2. \(r^4\)
3. \(r^3\)
4. \(r^2\)

A fluid is flowing through a horizontal pipe of varying cross-sections, with speed \(v\) ms^-1 at a point where the pressure is \(P\) pascal. At another point where pressure is \(\dfrac{P}{2}\) pascal, its speed is \(V\) ms^-1. If the density of the fluid is \(\rho\) kg-m^-3 and the flow is streamlined, then \(V\) is equal to:

A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by \(52\) K, its efficiency is doubled. The temperature in of the source will be:
1. \(52\) K
2. \(104\) K
3. \(156\) K
4. \(208\) K

The thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V₂ = 2V₁ then the ratio of temperature T₂/T₁ is :

1. $\frac{1}{2}$

2. 2

3. $\sqrt{2}$

4. $\frac{1}{\sqrt{2}}$

\(1\) mole of rigid diatomic gas performs a work of \(\dfrac{Q}{5}\) when heat \(Q\) is supplied to it. Change in internal energy of the gas is: