An engine pumps water continuously through a hose. Water leaves the hose with a velocity \(v\) and \(m\) is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

1. \(\dfrac{1}{2} m v^{3}\)                                   

2. \(m v^{3}\)

3. \(\dfrac{1}{2} m v^{2}\)                                   

4. \(\dfrac{1}{2} m^{2} v^{2}\)

Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is \(36~\text g\) and its density is \(9~\text{g/cm}^3.\) If the mass of the other is \(48~\text g,\) its density in \((\text{g/cm}^3)\) will be:
1. \(\frac{4}{3}\)
2. \(\frac{3}{2}\)
3. \(3\)
4. \(5\)

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. ${10}^5 \mathrm{N}/\mathrm{m}$                                 

2. $2\times {10}^5 \mathrm{N}/\mathrm{m}$

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

Equal masses of water and a liquid of relative density \(2\) are mixed together, then the mixture has a density of:
1. \(\dfrac{2}{3}\)

2. \(\dfrac{4}{3}\)

3. \(\dfrac{3}{2}\)

4. \(3\)

A body of density ${\mathrm{d}}_1$ is counterpoised by Mg of weights of density ${\mathrm{d}}_2$ in air of density d. Then the true mass of the body is

1. M                                   

2. $\mathrm{M}\left(1-\frac{\mathrm{d}}{{\mathrm{d}}_2}\right)$

3. $\mathrm{M}\left(1-\frac{\mathrm{d}}{{\mathrm{d}}_1}\right)$                       

4. $\frac{\mathrm{M}(1-\mathrm{d}/{\mathrm{d}}_2)}{(1-\mathrm{d}/{\mathrm{d}}_1)}$

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