Mechanical Properties of Fluids

Two spheres of equal masses but radii r₁ and r₂ are allowed to fall in a liquid of infinite column. The ratio of their terminal velocities is

• 1

• r₁ : r₂

• r₂ : r₁

• $\sqrt{{\mathrm{r}}_1} : \sqrt{{\mathrm{r}}_2}$

A liquid flows through two capillary tubes A and B connected in series. The length and radius of B are twice those of A. What is the ratio of the pressure difference across A to that across B ?

n identical droplets are charged to V volt  each. if they coalesce to form a single drop, then its potential will be

• n^2/3V

• n^1/3V

• nV

• V/n

A body floats in water with 40% of its volume outside water. When the same body floats in oil, 60% of its volume remains outside oil. The relative density of the oil is

• 0.9

• 1.2

• 1.5

• 1.8

A uniform long tube is bent into a circle of radius R and it lies in vertical plane. Two liquids of same volume but densities ρ and δ fill half the tube. The angle θ is

• ${\tan }^{-1} \left(\frac{\mathrm{\rho } - \mathrm{\delta }}{\mathrm{\rho } + \mathrm{\delta }}\right)$

• ${\tan }^{-1} \left(\frac{\mathrm{\rho }}{\mathrm{\delta }}\right)$

• ${\tan }^{-1} \left(\frac{\mathrm{\delta }}{\mathrm{\rho }}\right)$

• ${\tan }^{-1} \left(\frac{\mathrm{\rho } + \mathrm{\delta }}{\mathrm{\rho } - \mathrm{\delta }}\right)$

Two solid spheres of same metal but of mass M and 8M fall simultaneously on a viscous liquid and their terminal velocities are v and nv, then value of n is

• 16

• 8

• 4

• 2

A stone of relative density K is released from rest on the surface ofa lake. If viscous effects are ignored, the stone sinks in water with an acceleration of

• g (1 − K)

• g (1 + K)

• $\mathrm{g} \left(1 - \frac{1}{\mathrm{K}}\right)$

• $\mathrm{g} \left(1 + \frac{1}{\mathrm{K}}\right)$

An object weights m₁ in a liquid of density d₁ and that in liquid of density d₂ is m₂. The density d of the object is

• $\frac{{\mathrm{m}}_2{\mathrm{d}}_2 - {\mathrm{m}}_1{\mathrm{d}}_1}{{\mathrm{m}}_2 - {\mathrm{m}}_1}$

• $\frac{{\mathrm{m}}_1{\mathrm{d}}_1 - {\mathrm{m}}_2{\mathrm{d}}_2}{{\mathrm{m}}_{2 }- {\mathrm{m}}_1}$

• $\frac{{\mathrm{m}}_2{\mathrm{d}}_1 - {\mathrm{m}}_1{\mathrm{d}}_2}{{\mathrm{m}}_1 - {\mathrm{m}}_2}$

• $\frac{{\mathrm{m}}_1{\mathrm{d}}_2 - {\mathrm{m}}_2{\mathrm{d}}_1}{{\mathrm{m}}_1 - {\mathrm{m}}_2}$

A body floats in water with 40% of its volume outside water. When the same body floats in an oil. 60% of its volume remains outside oil. The relative density of oil is

• 0.9

• 1.0

• 1.2

• 1.5

Two soap bubbles of radii x and y coalesce to constitute a bubble of radius z. Then z is equal to 

• $\sqrt{{\mathrm{x}}^2 + {\mathrm{y}}^2}$

• $\sqrt{\mathrm{x} + \mathrm{y}}$

• x + y

• $\frac{\mathrm{x} + \mathrm{y}}{2}$