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 cm. If the elevator starts accelerating up, the reading will be
(1) Zero                                       

(2) Equal to 76 cm

(3) More than 76 cm                     

(4) Less than 76 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 beaker containing a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out, the pressure in the liquid near the bottom of the beaker will
1. Increase
2. Decrease
3. Remain constant
4. First decrease and then increase

A vertical U-tube of uniform inner cross section, contains mercury in both its arms. A glycerin (density = 1.3 g/${\mathrm{cm}}^3$) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/${\mathrm{cm}}^3$ is poured into the other arm until the upper surfaces of the oil and glycerin are at the same horizontal level. Find the length of the oil column. [Density of mercury = 13.6 g/${\mathrm{cm}}^3$]  
                       
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) $\mathrm{\rho }={\mathrm{\rho }}_0/\mathrm{\gamma } \mathrm{d\theta }$