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

• $\frac{\mathrm{x} + \mathrm{y}}{2}$

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