A square plate of 0.1 m side moves parallel to a second plate with a velocity of 0.1 m/s, both plates being immersed in water. If the viscous force is 0.002 N and the coefficient of viscosity is 0.01 poise, distance between the plates in m is

(1) 0.1                             

(2) 0.05

(3) 0.005                         

(4) 0.0005

Spherical balls of radius 'r' are falling in a viscous fluid of viscosity '$\mathrm{\eta }$' 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'.

A small sphere of mass m is dropped from a great height. After it has fallen 100 m, it has attained its terminal velocity and continues to fall at that speed. The work done by air friction against the sphere during the first 100 m of fall is

(1) Greater than the work done by air friction in the second 100 m

(2) Less than the work done by air friction in the second 100 m

(3) Equal to 100 mg

(4) Greater than 100 mg

A liquid is flowing in a horizontal uniform capillary tube under a constant pressure difference P. The value of pressure for which the rate of flow of the liquid is doubled when the radius and length both are doubled is

(a) P                             (b) $\frac{3\mathrm{P}}{4}$

(c) $\frac{\mathrm{P}}{2}$                           (d) $\frac{\mathrm{P}}{4}$

We have two (narrow) capillary tubes T₁ and T₂. Their lengths are l₁ and l₂ and radii of cross-section are r₁ and r₂ respectively. The rate of flow of water under a pressure difference P through tube T₁ is 8cm³/sec. If l₁ = 2l₂ and r₁ =r₂, what will be the rate of flow when the two tubes are connected in series and pressure difference across the combination is same as before (= P)

(a) 4 cm³/sec                           (b) (16/3) cm³/sec

(c) (8/17) cm³/sec                    (d) None of these

 As the temperature of water increases, its viscosity

(1) Remains unchanged

(2) Decreases

(3) Increases

(4) Increases or decreases depending on the external pressure

A small drop of water falls from rest through a large height h in air; the final velocity is

(1) $\propto \sqrt{\mathrm{h}}$

(2) $\propto \mathrm{h}$

(3) $\propto (1/\mathrm{h})$

(4) Almost independent of h

The rate of flow of liquid in a tube of radius r, length l, whose ends are maintained at a pressure difference P is $\mathrm{V}=\frac{{\mathrm{\pi QPr}}^4}{\mathrm{\eta l}}$ where $\mathrm{\eta }$ is coefficient of the viscosity and Q is-

(1) 8                     

(2) $\frac{1}{8}$

(3) 16                     

(4) $\frac{1}{16}$

Water flows in a streamlined manner through a capillary tube of radius a, the pressure difference being P and the rate of flow Q. If the radius is reduced to a/2 and the pressure increased to 2P, the rate of flow becomes

(1) $4\mathrm{Q}$                          

(2) $\mathrm{Q}$

(3) $\frac{\mathrm{Q}}{4}$                         

(4) $\frac{\mathrm{Q}}{8}$

What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are $\mathrm{\rho }$ and $\mathrm{\sigma }$ respectively, and the viscosity of the liquid is $\mathrm{\eta }$).

(1) $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}\left(\mathrm{\rho }-2\mathrm{\sigma }\right)$                     

(2) $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}\left(2\mathrm{\rho }-\mathrm{\sigma }\right)$

(3) $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}\left(\mathrm{\rho }-\mathrm{\sigma }\right)$                       

(4) $\frac{2{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}\left(\mathrm{\rho }-\mathrm{\sigma }\right)$