Mechanical Properties of Fluids

Air inside a closed container is saturated with water vapour. The air pressure is p and the saturated vapour pressure of water is $\overline{\mathrm{p}}$. If the mixture is compressed to one-half of its volume by maintammg temperature constant, the pressure becomes

• $\mathrm{2}\left(\mathrm{p} + \overline{\mathrm{p}}\right)$

• $2\mathrm{p} + \overline{\mathrm{p}}$

• $\left(\mathrm{p} + \overline{\mathrm{p}}\right)/2$

• $\mathrm{p} + 2\overline{\mathrm{p}}$

A diver at a depth of 12 m in water $\left(\mathrm{\mu } = \frac{4}{3}\right)$ sees the sky in a cone-of semivertical angle

• ${\sin }^{-1}\left(\frac{4}{3}\right)$

• ${\tan }^{-1}\left(\frac{4}{3}\right)$

• ${\sin }^{-1}\left(\frac{3}{4}\right)$

• 90°

Water is flowing through a very narrow tube. The velocity of water below which the flow remains a streamline flow is known as

• relative velocity

• terminal velocity

• critical velocity

• particle velocity

A body when fully immersed in a liquid of specific gravity 1.2 weighs 44 gwt. The same body when fully immersed in water weighs 50 gwt. The mass of the body is

• 36 g

• 48 g

• 64 g

• 80 g

The wettability of a surface by a liquid depends primarily on

• viscosity

• surface tension

• density

• angle of contact between the surface and the liquid

In the given (V-T) diagram, what is the relation between pressures p₁ and p₂ ?

• p₂ = p₁

• p₂ > p₁

• p₂ < p₁

• Cannot be predicted

A small metal sphere of radius a is falling with a velocity v through a vertical column of a viscous liquid. If the coefficient of viscosity of the liquid is η, then the sphere encounters an opposing force of

• $6{\mathrm{\pi \eta a}}^2\mathrm{v}$

• $\frac{6\mathrm{\eta v}}{\mathrm{\pi a}}$

• $6\mathrm{\pi \eta av}$

• $\frac{\mathrm{\pi \eta v}}{6{\mathrm{a}}^3}$

A drop of some liquid of volume 0.04 cm³ is placed on the surface of a glass slide. Then another glass slide is placed on it in such a way that the liquid forms a thin layer of area 20 cm² between the surfaces of the two slides. To separate the slides a force of 16 x10⁵ dyne has to be applied normal to the surfaces. The surface tension of the liquid is (in dyne-cm^-1)

• 60

• 70

• 80

• 90

To determine the composition of a bimetallic alloy, a sample is first weight in air and then in water. These weights are found to be w₁ and w₂ respectively. If the densities of the two constituents metals are ρ₁ and ρ₂ respectively, then the weight of the first metal in the sample is (where ρ_w is the density of water)

• $\frac{{\mathrm{\rho }}_1}{{\mathrm{\rho }}_{\mathrm{w}} \left({\mathrm{\rho }}_2 - {\mathrm{\rho }}_1\right)} \left[{\mathrm{w}}_1 \left({\mathrm{\rho }}_2 - {\mathrm{\rho }}_{\mathrm{w}}\right) - {\mathrm{w}}_2{\mathrm{\rho }}_2\right]$

• $\frac{{\mathrm{\rho }}_1}{{\mathrm{\rho }}_{\mathrm{w}} \left({\mathrm{\rho }}_2 + {\mathrm{\rho }}_1\right)} \left[{\mathrm{w}}_1 \left({\mathrm{\rho }}_2 - {\mathrm{\rho }}_{\mathrm{w}}\right) + {\mathrm{w}}_2{\mathrm{\rho }}_2\right]$

• $\frac{{\mathrm{\rho }}_1}{{\mathrm{\rho }}_{\mathrm{w}} \left({\mathrm{\rho }}_2 - {\mathrm{\rho }}_1\right)} \left[{\mathrm{w}}_1 \left({\mathrm{\rho }}_2 + {\mathrm{\rho }}_{\mathrm{w}}\right) - {\mathrm{w}}_2{\mathrm{\rho }}_1\right]$

• $\frac{{\mathrm{\rho }}_1}{{\mathrm{\rho }}_{\mathrm{w}} \left({\mathrm{\rho }}_2 - {\mathrm{\rho }}_1\right)} \left[{\mathrm{w}}_1 \left({\mathrm{\rho }}_1 - {\mathrm{\rho }}_{\mathrm{w}}\right) - {\mathrm{w}}_2{\mathrm{\rho }}_1\right]$

A 20 cm long capillary tube is dipped vertically in water and the liquid rises upto 10 cm. If the entire system is kept in a freely falling platform, the length of the water column in the tube will be

• 5 cm

• 10 cm

• 15 cm

• 20 cm