A tube of length L is filled completely with an incompressible liquid of mass M and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by liquid at the other end is

1.  $\frac{{\mathrm{M\omega }}^2\mathrm{L}}{2}$

2.  ${\mathrm{ML\omega }}^2$

3.  $\frac{{\mathrm{M\omega }}^2\mathrm{L}}{4}$

4.  $\frac{M{L}^2{\omega }^2}{2}$

The radius of a soap bubble is increased from R to 2 R. Work done in this process (T = surface tension) is

1.  $24 {\mathrm{\pi R}}^2\mathrm{T}$

2.  $48 {\mathrm{\pi R}}^2\mathrm{T}$

3.  $12 {\mathrm{\pi R}}^2\mathrm{T}$

4.  $36 {\mathrm{\pi R}}^2\mathrm{T}$

A small spherical solid ball is dropped in a viscous liquid. Its journey in the liquid is best described in the figure by :

1.  Curve A

2.  Curve B

3.  Curve C

4.  Curve D

Water flows through a frictionless duct with a cross-section varying as shown in the figure. Pressure p at points along the axis is represented by
                      

1. 2.

3.  4.

The area of cross-section of the wider tube shown in the figure is $800 {\mathrm{cm}}^2.$ If a mass of 12 kg is placed on the massless piston, the difference is heights h in the level of water in the two tubes is :

1.  10 cm

2.  6 cm

3.  15 cm

4.  2 cm

Equation of continuity based on :

1.  Conservation of mass

2.  Conservation of energy

3.  Conservation of angular momentum

4.  None of these

The weight of an aeroplane flying in the air is balanced by 

(1) Vertical component of the thrust created by air currents striking the lower surface of the wings

(2) Force due to reaction of gases ejected by the revolving propeller

(3) Upthrust of the air which will be equal to the weight of the air having the same volume as the plane

(4) Force due to the pressure difference between the upper and lower surfaces of the wings created by different air speeds on the surfaces

A U tube with both ends open to the atmosphere,is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is 

(a) $650 kg m^{-3}$

(b) $425 kg m^{-3}$

(c) $800 kg m^{-3}$

(d) $928 kg m^{-3}$

A rectangular film of liquid is extended from (4 cm$\times 2 cm$) to $\left(5 cm\times 4 cm\right)$. If the work done is $3\times {10}^{-4}$ J,the value of the surface tension of the liquid is 

(a) $0.250 N{m}^{-1}$

(b) $0.125 N{m}^{-1}$

(c) $0.2N{m}^{-1}$

(d) $8.0 N{m}^{-1}$

Three liquids of densities ${\rho }_1, {\rho }_2 and {\rho }_3$ (with ${\rho }_1>{\rho }_2>{\rho }_3$), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact ${\theta }_1,{\theta }_2 and {\theta }_3$ obey

(a) $\frac{\pi }{2}>{\theta }_1>{\theta }_2>{\theta }_3\ge 0$

(b) $0\le {\theta }_1<{\theta }_2<{\theta }_3<\frac{\pi }{2}$

(c) $\frac{\pi }{2}<{\theta }_1<{\theta }_2<{\theta }_3<\pi$

(d) $\pi >{\theta }_1>{\theta }_2>{\theta }_3>\frac{\pi }{2}$