11.

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

For a gas $\frac{\mathrm{R}}{{\mathrm{C}}_{\mathrm{v}}}$= 0.67. This gas is made up of molecules which are

• monoatomic

• polyatomic

• mixture of diatomic and polyatomic molecules

• diatomic

A transverse wave is represented by the equation   $\mathrm{y} = {\mathrm{y}}_{\mathrm{o}} \sin \frac{2\mathrm{\pi }}{\mathrm{\lambda }} \left(\mathrm{vt} - \mathrm{k}\right)$.  For what value of $\mathrm{\lambda }$ is the particle velocity equal to two times the wave velocity 

• $\mathrm{\lambda } = \mathrm{\pi } {\mathrm{y}}_{\mathrm{o}}$

• $\mathrm{\lambda } = \frac{\mathrm{\pi } {\mathrm{y}}_{\mathrm{o}}}{2}$

• $\mathrm{\lambda } = \frac{\mathrm{\pi } {\mathrm{y}}_{\mathrm{o}}}{3}$

• $\mathrm{\lambda } = 2\mathrm{\pi } \mathrm{i} {\mathrm{y}}_{\mathrm{o}}$

Two simple pendulums of length 0.5 m and 20 m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has
completed x oscillations, where k is

• 1

• 3

• 2

• 5

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

A black body has a wavelength of ) λ at temperature 2000 K. Its corresponding wavelength at temperature 3000 K will be

• $\frac{2 \mathrm{\lambda }}{3}$

• $\frac{3 \mathrm{\lambda }}{2}$

• $\frac{4 \mathrm{\lambda }}{9}$

• $\frac{9 \mathrm{\lambda }}{4}$

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%

A parallel palte condenser is filled with two dielectrics as shown in figure. Area of each pate is A m² and the separation is d metre. The dielectric constants are K₁ and K₂ respectively. Its capacitance in farad will be

• $\frac{2 {\mathrm{\epsilon }}_{\mathrm{o}}\mathrm{A}}{\mathrm{d}}\left(\frac{{\mathrm{K}}_1 + {\mathrm{K}}_2}{{\mathrm{K}}_1 {\mathrm{K}}_2}\right)$

• $\frac{2{\mathrm{\epsilon }}_{\mathrm{o}} \mathrm{A}}{\mathrm{d}} \left(\frac{{\mathrm{K}}_1 {\mathrm{K}}_2}{{\mathrm{K}}_1 + {\mathrm{K}}_2}\right)$

• $\frac{{\mathrm{\epsilon }}_{\mathrm{o}} \mathrm{A}}{\mathrm{d}} \left(\frac{{\mathrm{K}}_1 + {\mathrm{K}}_2}{2{\mathrm{K}}_1 {\mathrm{K}}_2}\right)$

• $\frac{{\mathrm{\epsilon }}_{\mathrm{o}} \mathrm{A} {\mathrm{K}}_1 {\mathrm{K}}_2}{2 \left({\mathrm{d}}_2 {\mathrm{K}}_1 + {\mathrm{d}}_1{\mathrm{K}}_2 \right)}$

A battery of emf 10 V and internal resistance of 0.5 ohm is connected across a variable resistance R. The maximum value of R is given by

• 0.5 Ω

• 1.00 Ω

• 2.0 Ω

• 0.25 Ω