The speed of air flows on the upper and lower surfaces of a wing of an aeroplane are v₁ and v₂ respectively. If A is the cross section area of the wing and ρ is the density of air, then the upward life is

• $\frac{1}{2}\mathrm{\rho } \mathrm{A}\left({\mathrm{v}}_2 - {\mathrm{v}}_1\right)$

• $\frac{1}{2}\mathrm{\rho } \mathrm{A}\left({\mathrm{v}}_1 + {\mathrm{v}}_2\right)$

• $\frac{1}{2} \mathrm{\rho } \mathrm{A} \left( {\mathrm{v}}_1^2 - {\mathrm{v}}_2^2 \right)$

• $\frac{1}{2}\mathrm{\rho } \mathrm{A} \left({\mathrm{v}}_1^2 + {\mathrm{v}}_2^2 \right)$

The work done in increasing the size of a soap film for 10cm × 6cm  to 10cm × 11cm is 3  × 10^-4 J. The surface tension of the film is

• 1.0  × 10^-2 N/m

• 6.0  × 10^-2 N/m

• 3.0  × 10^-2 N/m

• 1.5  × 10^-2 N/m

A balloon contains 500 m³ of helium at 27^o C and 1 atmosphere pressure. The volume of the helium at - 3° C temperature and 0.5 atmosphere pressure will be

• 1000 m³

• 900 m³

• 700 m³

• 500 m³

An ice-cube of density 900 kg/m³ is floating in water of density 1000 kg/m³. The percentage of volume ofice-cube outside the water is

• 20%

• 35%

• 10%

• 25%

The lower end of capillary tube is immersed in mercury. The level of mercury in the tube is found to be 2 cm below the outer level. If the same tube is immersed in water, upto what height will the water rise in the capillary?

• 5.9

• 4.9

• 2.9

• 1.9

116.

A capillary tube of length L and radius r is connected with another capillary tube of the same length but half the radius in series. The rate of steady volume flow of water through first capillary tube under a pressure difference of p is V. The rate of steady volume flow
through the combination will be (the pressure difference across the combination is p)

• 17 V

• $\frac{16}{17} \mathrm{V}$

• $\frac{\mathrm{V}}{17}$

• $\frac{17}{16} \mathrm{V}$

A small spherical drop fall from rest in viscous liquid. Due to friction, heat is produced. The correct relation between the rate of production of heat and the radius of the spherical drop at terminal velocity will be

• $\frac{\mathrm{dH}}{\mathrm{dt}} \propto \frac{1}{{\mathrm{r}}^5}$

• $\frac{\mathrm{dH}}{\mathrm{dt}} \propto {\mathrm{r}}^4$

• $\frac{\mathrm{dH}}{\mathrm{dt}} \propto \frac{1}{{\mathrm{r}}^4}$

• $\frac{\mathrm{dH}}{\mathrm{dt}} \propto {\mathrm{r}}^5$

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