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/${\mathrm{cm}}^3$]  
                       

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:

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

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

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

From the adjacent figure, 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

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: 

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/${\mathrm{m}}^3$) 

A hemispherical bowl just floats without sinking in a liquid of density $1.2\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$. If the outer diameter and the density of the material of the bowl are 1 m and $2\times {10}^4 \mathrm{kg}/{\mathrm{m}}^3$ respectively, then the inner diameter of the bowl will be:

In making an alloy, a substance of specific gravity ${\mathrm{s}}_1$ and mass ${\mathrm{m}}_1$ is mixed with another substance of specific gravity ${\mathrm{s}}_2$ and mass ${\mathrm{m}}_2$ ; then the specific gravity of the alloy is

A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3. For this sphere to float with its entire volume submerged underwater, the ratio of mass of concrete to mass of sawdust will be:

A metallic block of density 5 gm ${\mathrm{cm}}^{-3}$ and having dimensions 5 cm × 5 cm × 5 cm is weighed in water. Its apparent weight will be

When two small bubbles join to form a bigger one, energy is

A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of g/3, the fraction of volume immersed in the liquid will be

A silver ingot weighing 2.1 kg is held by a string so as to be completely immersed in a liquid of relative density 0.8. The relative density of silver is 10.5. The tension in the string in kg-wt is

Two solids A and B float in water. It is observed that A floats with half its volume immersed and B floats with 2/3 of its volume immersed. Compare the densities of A and B

The fraction of a floating object of volume ${\mathrm{V}}_0$ and density ${\mathrm{d}}_0$ above the surface of a liquid of density d will be

Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This law was first formulated by:

 A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body ?

A cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with acceleration downwards, the length of spring

A solid sphere of density $\mathrm{\eta }$ ( > 1) times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the sphere is m, then the tension in the string is given by:

A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water ?

A ball whose density is $0.4\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$ falls into water from a height of 9 cm . To what depth does the ball sink

A boat carrying steel balls is floating on the surface of water in a tank. If the balls are thrown into the tank one by one, how will it affect the level of water ?

Two pieces of metal when immersed in a liquid have equal upthrust on them; then

A candle of diameter d is floating on a liquid in a cylindrical container of diameter D (D>>d) as shown in figure. If it is burning at the rate of 2cm/hour then the top of the candle will:
            

Construction of submarines is based on 

In which one of the following cases will the liquid flow in a pipe be most streamlined  ?

Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. The velocity of flow of water in the pipe of 2 cm diameter is -