A spherical ball of radius \(r\) is falling in a viscous fluid of viscosity \(\eta\) with a velocity \(v.\) The retarding viscous force acting on the spherical ball is:

1.	inversely proportional to \(r\) but directly proportional to velocity \(v.\)
2.	directly proportional to both radius \(r\) and velocity \(v.\)
3.	inversely proportional to both radius \(r\) and velocity \(v.\)
4.	directly proportional to \(r\) but inversely proportional to \(v.\)

The pans of a physical balance are in equilibrium. If Air is blown under the right hand pan then the right hand pan will:

A sniper fires a rifle bullet into a gasoline tank making a hole 53.0 m below the surface of gasoline. The tank was sealed at 3.10 atm. The stored gasoline has a density of 660 ${\mathrm{kgm}}^{-3}$. The velocity with which gasoline begins to shoot out of the hole will be:
 

A tank is filled with water up to a height \(\mathrm H.\) Water is allowed to come out of a hole \(\mathrm P\) in one of the walls at a depth \(\mathrm D\) below the surface of water. Express the horizontal distance \(\mathrm{x}\) in terms of \(\mathrm H\) and \(\mathrm {D}\text :\)
                    

1. $\mathrm{x}=\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

2. $\mathrm{x}=\sqrt{\frac{\mathrm{D}(\mathrm{H}-\mathrm{D})}{2}}$

3. $\mathrm{x}=2\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

4. $\mathrm{x}=4\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

If a small drop of water falls from rest through a large height h in air, then the final velocity is:

A block of ice floats on a liquid of density 1.2 $g/c{m}^3$ in a beaker. The level of liquid when ice completely melts-

1. Remains same                         

2. Rises

3. Lowers                                   

4. (1), (2) or (3)

In order to float a ring of area 0.04 ${\mathrm{m}}^2$ in a liquid of surface tension 75 N/m, the required surface energy will be:

If pressure at half the depth of a lake is equal to 2/3^rd the pressure at the bottom of the lake, then the depth of the lake is:

A spherical drop of water has a radius of 1 mm. If the surface tension of water is $70\times {10}^{-3}$ N/m, the difference in pressures inside and outside the spherical drop is:

In a capillary tube, pressure below the curved surface of the water will be: