If an incompressible liquid is flowing through a horizontal pipe having branches of area \(\mathrm{A},\) \(0.4\mathrm{A},\) and \(0.5\mathrm{A}\) as shown in the figure, then the value of \(\mathrm{v}\) is:
                               
1. 3.2 m/s
2. 6.4 m/s
3. 1.6 m/s
4. 0.8 m/s

A U tube is partially filled with water. Oil which is immiscible in water is poured into one side until the water rises by 25 cm on the other side. If the oil level is 12.5 cm higher than the water level, then the relative density of the oil is:

1. 0.3

2. 0.5

3. 0.8

4. 1.2

An airplane of a total wing area of \(120\) ${\mathrm{m}}^2$ is in a level flight at some height. If the pressure difference between the upper and lower surface is \(2.5\) kPa, then the mass of the airplane is: (Take \(g=10\) ${\mathrm{ms}}^{-2}$)

An air bubble of radius r in water is at a certain depth below the water surface. If P is the pressure inside the bubble, then the depth below the water surface is: [\(P_{0}\) = Atmospheric pressure, \(\rho\) = Density of water, T = surface tension of water]

1.  \(\frac{P   -   P_{0}}{ρg}   -   \frac{4 T}{rρg}\)

2.  \(\frac{P   +   P_{0}}{ρg}   +   \frac{2 T}{rρg}\)

3.  \(\frac{P   -   P_{0}}{ρg}   -   \frac{2 T}{rρg}\)

4.  \(\frac{P   -   P_{0}}{ρg}   +   \frac{2 T}{2 rρg}\)

A block weighs 5 N in air and 4.5 N in a liquid of specific gravity 0.5. Its weight in water will be:

1. 3.5 N

2. 4.0 N

3. 2.5 N

4. 3.0 N

A liquid is poured into three vessels of the same base area and equal heights as shown in the figure, then:
                                  

A liquid is filled in a container as shown in the figure. The force exerted by the liquid on the base of the container must be:
                                 

The surface tension of a liquid is \(5\) N m^-1. If a film is held on a ring of area \(0.02\) ${\mathrm{m}}^2$, then its total surface energy is:
1. \(3\times\) ${10}^{-2}$ J
2. \(2\times\) ${10}^{-1}$ J
3. \(3\times\) ${10}^{-3}$J
4. ${10}^{-1}$ J

A liquid filled in a container has plane meniscus. If $\mathrm{\theta }$ is the angle of contact, then:
1. $\mathrm{\theta }$ = \(0^\circ\)
2. $\mathrm{\theta }$ = \(90^\circ\)
3. $\mathrm{\theta }$ < \(90^\circ\)
4. $\mathrm{\theta }$ = \(180^\circ\)

The relative velocity of two adjacent layers of a liquid is 6 cm/s and the perpendicular distance between layers is 0.1 mm. The velocity gradient for liquid (in per second) is: