21.

Universal time is based on

• rotational effect of the earth about its axis

• vibrations of cesium atom

• orbital motion of the earth around the sun

• oscillation of quartz crystal

A diatomic gas (γ = 1.4) does 200 J of work when it is expanded isobarically. Find the heat given to the gas in the process

• 500 J

• 700 J

• 600 J

• 900 J

The earth receives solar radiation at a rate of 8.2 J cm^-2 min^-1. If the sun radiates as the black bodies, the temperature at the surface of the sun will be (the angle subtended by sun on the earth in suppose 0.53° and Stefan constant is σ = 5.67x 10^-6 Wm³ K⁴

• 5800 K

• 6700 K

• 8000 K

• 7800 K

A horizontal tube of length l closed at both ends, contains an ideal gas of molecular weight M. The tube is rotated at a constant angular velocity ω about a vertical axis passing through an end. Assuming the temperature to be uniform and constant. If p₁ and p₂ denote the pressure at free and the fixed end respectively, then choose the correct relation

• $\frac{{\mathrm{p}}_2}{{\mathrm{p}}_1} = {\mathrm{e}}^{\frac{{\mathrm{M\omega }}^2 {\mathrm{l}}^2}{2^{\mathrm{RT}}}}$

• $\frac{{\mathrm{p}}_1}{{\mathrm{p}}_2} = {\mathrm{e}}^{\frac{\mathrm{M} {\mathrm{\omega l}}^2}{\mathrm{RT}}}$

• $\frac{{\mathrm{p}}_1}{{\mathrm{p}}_2} = {\mathrm{e}}^{\frac{\mathrm{\omega } \mathrm{l} \mathrm{M}}{3\mathrm{RT}}}$

• $\frac{{\mathrm{p}}_2}{{\mathrm{p}}_1} = {\mathrm{e}}^{\frac{{\mathrm{M}}^{2 }{\mathrm{\omega }}^{2 }{\mathrm{l}}^2}{3\mathrm{RT}}}$

1 kg of water is converted into steam at the same temperature and at 1 atm (100 kPa). The density of water and steam are 1000 kgm^-3 and 0.6 kgm^-3 respectively. The latent heat of vaporisation of water is 2.25 x 10⁶ J kg^-1, What will be increase in energy?

• 3 × 10⁵ J

• 4 × 10⁶ J

• 2.08 × 10⁶ J

• None of these

A lead ball at 30°C is dropped from a height of 6.2 km. The ball is heated due to the air resistance and it completely melts just before reaching the ground. The molten substance falls slowly on the ground. If the specific heat of lead = 126 Jkg^-1 oC^-1 and melting point of lead= 130°C and suppose that any mechanical energy lost is used to heat the ball, then the latent heat of fusion of lead is

• 2.4 × 10⁴ J Kg^-1

• 3.6 × 10⁴ J Kg^-1

• 7.6 × 10² J kg^-1

• 4.94 × 10³ J kg^-1

A particle is subjected to two simple harmonic motions along X-axis while other is along a line making angle 45° with the X-axis. The two motions are given by   x = x₀ sin ωt  and  s =s₀ sin ωt. The amplitude of resultant motion is 

• x₀ + s₀ + 2x₀s₀

• $\sqrt{{\mathrm{x}}_0^2 + {\mathrm{s}}_0^2}$

• $\sqrt{{\mathrm{x}}_0^2 - {\mathrm{s}}_0^2 + 2{\mathrm{x}}_0 {\mathrm{s}}_0}$

• ${\left[{\mathrm{x}}_0^2 + {\mathrm{s}}_0^2 + \sqrt{2} {\mathrm{x}}_0 {\mathrm{s}}_0\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

What is the change in the volume of 1.0 L kerosene, when it is subjected to an extra pressure of 2.0 x 10⁵ Nm^-2 from the following data? Density of kerosene = 800 kg m^-3  and speed of sound in kerosene= 1330 ms^-1.

• 0.97 cm^-3

• 0.66 cm^-3

• 0.15 cm^-3

• 0.59 cm^-3

A 4 kg block is suspended from the ceiling of an elevator through a spring having a linear mass density of 19.2 x 10^-3 kg m^-3 . Find the speed with respect to spring with which a wave pulse can proceed on the spring if the elevator accelerates up at the rate of 2.0 ms^-2.
Take g = 10 ms^-2

• 30 m/s

• 42 m/s

• 46 m/s

• 50 m/s

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