The change in the value of g at a height ‘h’ above the surface of the earth is the same as at a depth ‘d’ below the surface of earth. When both ‘d’ and ‘h’ are much smaller than the radius of earth, then which one of the following is correct?

• d =h/2

• d=3h/2

• d =2h

• d =2h

22.

A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between
(you may take G = 6 . 67× 10^-11 Nm²/ kg²)

• 13.34 x 10^-10 J

• 3.33 x 10^-10 J

• 6.67 x10^-9 J

• 6.67 x10^-9 J

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

• 8 cm

• 10 cm

• 4 cm

• 4 cm

If S is stress and Y is Young’s modulus of material of a wire, the energy stored in the wire per unit volume is

• 2S²Y

• S²/2Y

• 2Y/S²

• 2Y/S²

Which of the following is incorrect regarding the first law of thermodynamics?

• It introduces the concept of internal energy

• It introduces the concept of entropy

• It is not applicable of any cyclic process

• It is not applicable of any cyclic process

A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio c_p/c_v of the mixture is

• 1.59

• 1.62

• 1.4

• 1.4

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

• 1/2

• 1/4

• 1/3

• 1/3

The figure shows a system of two concentric spheres of radii r₁ and r₂ and kept at temperatures T₁ and T₂ respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to

A system goes from A to B via two processes I and II as shown in the figure. If ∆U₁ and ∆U₂ are the changes in internal energies in the processes I and II respectively, the

• ∆U₁ = ∆U₂

• relation between ∆U₁ and ∆U₂ can not be determined

• ∆U₂ > ∆U₁

• ∆U₂ > ∆U₁

The function sin²(ωt) represents

• a periodic, but not simple harmonic motion with a period 2π/ω

• a periodic, but not simple harmonic motion with a period π/ω

• a simple harmonic motion with a period 2π/ω

• a simple harmonic motion with a period 2π/ω