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

A vertical $\mathrm{U}$-tube of uniform inner cross-section contains mercury in both its arms. A glycerin (density$=1.3$ g/cm³) column of length $10$ cm is introduced into one of its arms. Oil of density $0.8$ g/cm³  is poured into the other arm until the upper surfaces of the oil and glycerin are at the same horizontal level. The length of the oil column is:
(density of mercury $=13.6$ g/cm³)
                       
1. $10.4$ cm
2. $8.2$ cm
3. $7.2$ cm
4. $9.6$ cm

A triangular lamina of area A and height h is immersed in a liquid of density $\mathrm{\rho }$ in a vertical plane with its base on the surface of the liquid. The thrust on the lamina is:
1. $\frac{1}{2}\mathrm{A\rho gh}$                 

2. $\frac{1}{3}\mathrm{A\rho gh}$

3. $\frac{1}{6}\mathrm{A\rho gh}$                 

4. $\frac{2}{3}\mathrm{A\rho gh}$

If two liquids of same masses but densities ${\mathrm{\rho }}_1$ and ${\mathrm{\rho }}_2$ respectively are mixed, then density of mixture is given by

1. $\mathrm{\rho }=\frac{{\mathrm{\rho }}_1+{\mathrm{\rho }}_2}{2}$                             

2. $\mathrm{\rho }=\frac{{\mathrm{\rho }}_1+{\mathrm{\rho }}_2}{2{\mathrm{\rho }}_1{\mathrm{\rho }}_2}$

3. $\mathrm{\rho }=\frac{2{\mathrm{\rho }}_1{\mathrm{\rho }}_2}{{\mathrm{\rho }}_1+{\mathrm{\rho }}_2}$                             

4. $\mathrm{\rho }=\frac{{\mathrm{\rho }}_1{\mathrm{\rho }}_2}{{\mathrm{\rho }}_1+{\mathrm{\rho }}_2}$

The density $\mathrm{\rho }$ of water of bulk modulus B at a depth y in the ocean is related to the density at surface ${\mathrm{\rho }}_0$ by the relation

1. $\mathrm{\rho }={\mathrm{\rho }}_0\left[1-\frac{{\mathrm{\rho }}_0\mathrm{gy}}{\mathrm{B}}\right]$                           

2. $\mathrm{\rho }={\mathrm{\rho }}_0\left[1+\frac{{\mathrm{\rho }}_0\mathrm{gy}}{\mathrm{B}}\right]$

3. $\mathrm{\rho }={\mathrm{\rho }}_0\left[1+\frac{\mathrm{B}}{{\mathrm{\rho }}_0\mathrm{gy}}\right]$                             

4. $\mathrm{\rho }={\mathrm{\rho }}_0\left[1-\frac{\mathrm{B}}{{\mathrm{\rho }}_0\mathrm{gy}}\right]$