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 $76~\text{cm}$