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

With rise in temperature, density of a given body changes according to one of the following relations

(a) $\mathrm{\rho }={\mathrm{\rho }}_0\left[1+\mathrm{\gamma } \mathrm{d\theta }\right]$                        (b) $\mathrm{\rho }={\mathrm{\rho }}_0\left[1-\mathrm{\gamma } \mathrm{d\theta }\right]$

(c) $\mathrm{\rho }={\mathrm{\rho }}_0\mathrm{\gamma } \mathrm{d\theta }$                                (d) $\mathrm{\rho }={\mathrm{\rho }}_0/\mathrm{\gamma } \mathrm{d\theta }$

For the figures given below, the correct observation is: