Mechanical Properties of Fluids

A tank of height H is fully filled with water. If the water rushing from a hole made in the tank below the free surface, strikes the floor at maximum horizontal distance, then the depth of the hole from the free surface must be

• $\left(\frac{3}{4}\right) \mathrm{H}$

• $\left(\frac{2}{3}\right) \mathrm{H}$

• $\left(\frac{1}{4}\right) \mathrm{H}$

• $\left(\frac{1}{2}\right) \mathrm{H}$

Water rises in a capillary tube to a height h. Choose false statement regarding capillary rise from the following

• On the surface of Jupiter, height will be less than h

• In a lift moving up with constant acceleration height is less than h

• On the surface of moon the height is more than h

• In a lift moving down with constant acceleration height is less than h

The pressure inside two soap bubbles is 1.01 and 1.02 atmosphere respectively. The ratio of their respective volumes is

• 2

• 4

• 6

• 8

A solid sphere of volume V and density ρ floats at the interface of two immiscible liquids of densities ρ₁ and ρ₂ respectively. If ρ₁ < ρ₂, then the ratio of volume of the parts of the sphere in upper and lower liquids is 

• $\frac{\mathrm{\rho } - {\mathrm{\rho }}_2}{{\mathrm{\rho }}_1 - \mathrm{\rho }}$

• $\frac{{\mathrm{\rho }}_2 - \mathrm{\rho }}{\mathrm{\rho } - {\mathrm{\rho }}_1}$

• $\frac{\mathrm{\rho } + {\mathrm{\rho }}_1}{\mathrm{\rho } + {\mathrm{\rho }}_2}$

• $\frac{\mathrm{\rho } + {\mathrm{\rho }}_2}{\mathrm{\rho } + {\mathrm{\rho }}_1}$

Radius of an air bubble at the bottom of the lake is r and it becomes 2r when the air bubble rises to the top surface of the lake. If P cm of water be the atmospheric pressure, then the depth of the lake is

• 2P

• 8P

• 4P

• 7P

A manometer connected to a closed tap reads 4.5 × 10⁵ Pa. When the tap is opened the reading of the manometer falls to 4 x 10⁵ Pa. Then the velocity of flow of water is

• 7 ms^-1

• 8 ms^-1

• 10 ms^-1

• 12 ms^-1

What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are ρ and σ respectively, and the viscosity of the liquid is η)

• $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }} \left(\mathrm{\rho } - 2\mathrm{\sigma }\right)$

• $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }} \left(2\mathrm{\rho } - \mathrm{\sigma }\right)$

• $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }} \left(\mathrm{\rho } - \mathrm{\sigma }\right)$

• $\frac{2{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }} \left(\mathrm{\rho } - \mathrm{\sigma }\right)$

A soap bubble in air (two surfaces) has surface tension 0.03 Nm^-1. Find the gauge pressure inside a bubble of diameter 30 mm.

• 2 Pa

• 4 Pa

• 8 Pa

• 10 Pa

A piece of ice is floating in a jar containing water. When the ice melts then the level of water

• rises

• falls

• remains unchanged

• rises or falls

A 10 cm³ cube floats in water with a height of 4 cm³ remaining above the surface. The density of the material from which the cube is made is

• 0.6 g cm^-3

• 1.0 g cm^-3

• 0.4 g cm^-3

• 0.24 g cm^-3