If two capillary tubes of radii r₁ and r₂ in the ratio 1 : 2 are dipped vertically in water, then the ratio of capillary rises in the respective tubes is

• 1 : 4

• 4 : 1

• 1 : 2

• 2 : 1

If the excess pressure inside a soap bubble of radius r₁ in air is equal to the excess pressure inside air bubble of radius r₂ inside the soap solution, then r₁ : r₂ is

• 2 : 1

• 1 : 2

• 1 : 4

• $\sqrt{2} : 1$

The pressure at depth h below the surface of a liquid of density ρ open to the atmosphere is

• greater than the atmospheric pressure by ρgh

• less than the atmospheric pressure by ρgh

• equal to the atmospheric pressure

• decreases exponentially with depth

1 cc of water becomes 1681 cc of steam when boiled at a pressure of10⁵ Nm^-2. The increasing internal energy of the system is (Latent heat of steam is 540 cal g^-1 , 1 cal = 4.2 J)

• 300 cal

• 500 cal

• 225 cal

• 600 cal

A partition wall has two layers of different
materials A and B in contact with each other.
They have the same thickness but the thermal conductivity of layer A is twice that of layer B. At steady state if the temperature difference across the layer B is 50 K, then the corresponding difference across the layer A is

• 50 K

• 12.5 K

• 16.6 K

• 60 K

Identify the wrong statement

• For isothermal process, ΔT = 0

• For isochoric process, ΔV = 0

• For cyclic process, ΔW = 0

• For adiabatic process, ΔQ = 0

27.

If the pressure and the volume of certain quantity of ideal gas are halved, then its temperature

• is doubled

• becomes one-fourth

• remains constant

• is halved

Two pendulums of lengths 1.44 m and 1 m start to swing together. The number of vibrations after which they will again start swinging together is

• 4

• 3

• 5

• 2

The average total energy in one time period of a particle of mass m executing SHM of amplitude a and angular velocity ω is

• $\frac{1}{2} {\mathrm{m\omega }}^2{\mathrm{a}}^2$

• $\frac{1}{4} {\mathrm{m\omega }}^2{\mathrm{a}}^2$

• 0

• mω²a²

Which one of the following is simple harmonic ?

• Rotation of earth around the sun

• Rotation of earth about its own axis

• Motion of oscillating liquid column in U-tube

• Motion of a steel ball in a viscous medium