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

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

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

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

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

Assertion:  A needle placed carefully on the surface of water may float, whereas the ball of the same material will always sink. 

Reason:  The buoyancy of an object depends both on the materials and shape of the object.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

A cylindrical tank is filled with water to level of 3 m. A hole is opened at height of 52.5 cm from bottom. The ratio of the area of the hole to that of cross-sectional area of the cylinder is 0.1. The square of the speed with which water is coming out from the orifice is (Take g = 10 m s^-2)

• 50 m² s^-2

• 40 m² s^-2

• 51.5 m² s^-2

• 50.5 m² s^-2

44.

Viscous force exerted by the liquid flowing between two plates in a streamline flow depends upon the

• velocity gradient in the direction perpendicular to the plates

• area of plate

• co-efficient of viscosity of the liquid

• all of these

Assertion: When height of a tube is less than liquid rise in the capillary tube, the liquid does not overflow. 

Reason: Product of radius of meniscus and height of liquid in the capillary tube always remain constant.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• f both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

A spherical body of diameter D is falling in viscous medium. Its terminal velocity is proportional to

• V_t ∝ D^1/2

• V_t ∝ D^3/2

• V_t ∝ D²

• V_t ∝ D^5/2

Assertion:  Surface energy of an oil drop is same whether placed on glass or water surface. 

Reason:  Surface energy is dependent only on the properties of oil.

• If both assertion and reason are true and reason is the correct explanation of assertion.
  
  

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Assertion:  Turbulence is always dissipative. 

Reason: High reynold number promotes turbulence.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

Pressure head in Bernoulli's equation is

• $\frac{\mathrm{P} \mathrm{\rho }}{\mathrm{g}}$

• $\frac{\mathrm{P}}{\mathrm{\rho } \mathrm{g}}$

• ρ g

• Pρg

Two spherical soap bubbles of radii a and b in vacuum coaleasce under isothermal conditions. The resulting bubbles has a radius given by

• $\frac{\left(\mathrm{a} + \mathrm{b}\right)}{2}$

• $\frac{\mathrm{ab}}{\mathrm{a} + \mathrm{b}}$

• $\sqrt{{\mathrm{a}}^2 + {\mathrm{b}}^2}$

• a+ b