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 area of cross-section of the wider tube shown in the figure is \(800~\text{cm}^2.\) If a mass of \(12~\text{kg}\) is placed on the massless piston, then the difference in heights \(h\) of the levels of water in the two tubes will be:

The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 x 10^-11 Pa^-1 and density of water is 10³kg/m³. What fractional compression of water will be obtained at the bottom of the ocean?

1. 0.8 x 10^-2
 

2. 1.0 x 10^-2 
 

3. 1.2 x 10^-2  
 

4. 1.4 x 10^-2 

The heart of a man pumps 5 L of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury is \(13.6\times 10^3\)kg/m³ and g =10 m/s², then the power of heart in watt is:
1. 1.70
2. 2.35
3. 3.0
4. 1.50

An inverted bell lying at the bottom of a lake 47.6 m deep has 50 cm³ of air trapped in it. The bell is brought to the surface of the lake. The volume of the trapped air will be (atmospheric pressure = 70 cm of Hg and density of Hg = 13.6 g/cm³) 
1. 350 cm³                               

2. 300 cm³

3. 250 cm³                               

4. 22 cm³

A siphon in use is demonstrated in the following figure. The density of the liquid flowing in siphon is 1.5 gm/cc. The pressure difference between the point P and S will be

1. ${10}^5<mspace\; width="1em"></mspace>\mathrm{N}/\mathrm{m}$                                 

2. $2\times {10}^5<mspace\; width="1em"></mspace>\mathrm{N}/\mathrm{m}$

3. Zero                                       

4. Infinity 

The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air is ${10}^4$. The height of the hill is
1. 250 m                             

2. 2.5 km

3. 1.25 km                           

4. 750 m

The value of g at a place decreases by 2%. The barometric height of mercury
1. Increases by 2%

2. Decreases by 2%

3. Remains unchanged

4. Sometimes increases and sometimes decreases
 

A barometer kept in a stationary elevator reads \(76~\text{cm}\). If the elevator starts accelerating up, the reading will be:
1. Zero
2. Equal to \(76~\text{cm}\)
3. More than \(76~\text{cm}\)
4. Less than \(76~\text{cm}\)

A closed rectangular tank is completely filled with water and is accelerated horizontally with an acceleration a towards right. Pressure is (i) maximum at, and (ii) minimum at

1. (i) B (ii) D

2. (i) C (ii) D

3. (i) B (ii) C

4. (i) B (ii) A