Mechanical Properties of Fluids

A boy can reduce the pressure in his lungs to 750 mm of mercury. Using a straw he can drink wacer from a glass upto the maximum depth of (atmospheric pressure = 760 mm of mercury; density of mercury = 13.6 gcm^-3)

• 13.6 cm

• 9.8 cm

• 10 cm

• 76 cm

Three capillary tubes of same length but internal radii 0.3 mm, 0.45 mm and 0.6 mm are connected in series and a liquid flows steadily through them. If the pressure difference across the third capillary is 8.1 mm of mercury, the pressure difference across the first capillary (in mm of mercury) is

• 16.2

• 32.4

• 129.6

• 2.025

A ring cut with an inner radius 4.85 cm and outer radius 4.95 cm is supported horizontally from one of the pans of a balance so that it comes in contact with the water in a vessel. If surface tension of water is 70 x 10^-3 Nm^-1,then the extra mass in the other pan required to pull the ring away from water is

• 2 g

• 3 g

• 4.4 g

• 15 g

If two capillary tubes of radii r₁ and r₂ in the ratio 1 : 2 are dipped vertically in water, then the ratio of capillary rises in the respective tubes is

• 1 : 4

• 4 : 1

• 1 : 2

• 2 : 1

If the excess pressure inside a soap bubble of radius r₁ in air is equal to the excess pressure inside air bubble of radius r₂ inside the soap solution, then r₁ : r₂ is

• 2 : 1

• 1 : 2

• 1 : 4

• $\sqrt{2} : 1$

The pressure at depth h below the surface of a liquid of density ρ open to the atmosphere is

• greater than the atmospheric pressure by ρgh

• less than the atmospheric pressure by ρgh

• equal to the atmospheric pressure

• decreases exponentially with depth

The average depth of Indian ocean is about 3000 m. The fractional compression, $\frac{∆\mathrm{V}}{\mathrm{V}}$ of water at the bottom of the ocean (given that the bulk modulus of the water = 2.2 × 10² Nm^-2 and g = 10 ms^-2) is

• 0.82 %

• 0.91 %

• 1.36 %

• 1.24 %

The terminal speed of a sphere of gold (density = 19.5 kg-m^-3) is 0.2 ms^-1 in a viscous liquid (density = 1.5 kg m^-3). Then the terminal speed of a sphere of silver (density = 10.5 kg m^-3) of the same size in the same liquid is 

• 0.1 ms^-1

• 1.133 ms^-1

• 0.4 ms^-1

• 0.2 ms^-1

A large open tank has two holes in its wall. One is a square hole of side a at a depth of x from the top and the other is a circular hole of radius r at a depth 4x from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then r is equal to

• $2\mathrm{\pi a}$

• a

• $\frac{\mathrm{a}}{\sqrt{2\mathrm{\pi }}}$

• $\frac{\mathrm{a}}{\mathrm{\pi }}$

Ice pieces are floating in a beaker A containing water and also in a beaker B containing miscible liquid of specific gravity 1.2. When ice melts, the level of

• water increases in A

• water decreases in A

• liquid in B decreases

• liquid in B increases