In the following fig. is shown the flow of liquid through a horizontal pipe. Three tubes A, B and C are connected to the pipe. The radii of the tubes A, B and C at the junction are respectively 2 cm, 1 cm and 2 cm. It can be said that the

 

(a) Height of the liquid in the tube A is maximum

(b) Height of the liquid in the tubes A and B is the same

(c) Height of the liquid in all the three tubes is the same

(d) Height of the liquid in the tubes A and C is the same

 

A manometer connected to a closed tap reads $3.5\times {10}^5 \mathrm{N}/{\mathrm{m}}^2$. When the valve is opened, the reading of manometer falls to $3.0\times {10}^5 \mathrm{N}/{\mathrm{m}}^2$ , then velocity of flow of water is
(1) 100 m/s                                       

(2) 10 m/s

(3) 1 m/s                                           

(4) $10\sqrt{10}$ m/s

A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in m/s) through a small hole on the side wall of the cylinder near its bottom is
(1) 10                                       

(2) 20

(3) 25.5                                     

(4) 5

There is a hole in the bottom of tank having water. If total pressure at bottom is 3 atm ($1 \mathrm{atm}={10}^5 \mathrm{N}/{\mathrm{m}}^2$) then the velocity of water flowing from hole is 

(a) $\sqrt{400}$ m/s             (b) $\sqrt{600}$ m/s

(c) $\sqrt{60}$ m/s                (d) None of these

A cylindrical tank has a hole of $1 {\mathrm{cm}}^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $70 {\mathrm{cm}}^3/\sec$. then the maximum height up to which water can rise in the tank is
(1) 2.5 cm                                             

(2) 5 cm

(3) 10 cm                                               

(4) 0.25 cm

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

Two drops of the same radius are falling through air with a steady velocity of 5 cm per sec. If the two drops coalesce, the terminal velocity would be 

(a) 10 cm per sec                                  (b) 2.5 cm per sec
(c) $5\times (4{)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ cm per sec                          (d) $5\times \sqrt{2}$ cm per sec

The rate of steady volume flow of water through a capillary tube of length 'l' and radius 'r' under a pressure difference of P is V. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is P)

(1) $\frac{\mathrm{V}}{16}$                                     

(2) $\frac{\mathrm{V}}{17}$

(3) $\frac{16\mathrm{V}}{17}$                                   

(4) $\frac{17\mathrm{V}}{16}$