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

For the figures given below, the correct observation is:
              

A given shaped glass tube having uniform cross section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity $\mathrm{\omega }$ then

(1) Water levels in both sections A and B go up

(2) Water level in Section A goes up and that in B comes down

(3) Water level in Section A comes down and that in B it goes up

(4) Water levels remains same in both sections

An iceberg of density 900 kg/${\mathrm{m}}^3$ is floating in water of density 1000 Kg/${\mathrm{m}}^3$. The percentage of volume of ice-cube outside the water is: 
1. 20%                                       
2. 35%
3. 10%                                       
4. 25%

A log of wood of mass 120 Kg floats in water. The weight that can be put on the raft to make it just sink, should be (density of wood = 600 Kg/${\mathrm{m}}^3$) 
(1) 80 Kg                                                 

(2) 50 Kg

(3) 60 Kg                                                 

(4) 30 Kg