31.

When the temperature of an ideal gas is increased from 27°C to 227°C, its rms speed is changed from 400 metre/sec to v_s. The v_s is :

• 516 m/s

• 450 m/s

• 310 m/s

• 746 m/s

To make the frequency double of a spring oscillator, we have to :

• reduce the mass to one fourth

• quadruple the mass

• double the mass

• half the mass

A particle executing SHM has amplitude 0.01 m and frequency 60 Hz. The maximum acceleration of the particle is :

• $60{\mathrm{\pi }}^2 \mathrm{m}/{\mathrm{s}}^2$

• $80{\mathrm{\pi }}^2 \mathrm{m}/{\mathrm{s}}^2$

• $120{\mathrm{\pi }}^2 \mathrm{m}/{\mathrm{s}}^2$

• $144{\mathrm{\pi }}^2 \mathrm{m}/{\mathrm{s}}^2$

When a wave travels in a medium, the particle's displacement is given by the equation

y = 0.03 sin(2t - 0.01 x)

where x and y are in metre and t in second. The wavelength of the wave is :

• 200 m

• 100 m

• 20 m

• 10 m

If 300 ml of a gas at 27° C is cooled to 7° C at constant pressure, then its final volume will be

• 540 mL

• 350 mL

• 280 mL

• 135 mL

When sound waves travel from air to water, which one of the following remains constant?

• Time period

• Frequency

• Velocity

• Wavelength

Universal gas constant is :

• $\frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{v}}}$

• C_p - C_v

• C_P + C_V

• $\frac{{\mathrm{C}}_{\mathrm{V}}}{{\mathrm{C}}_{\mathrm{P}}}$

A gas at state A changes to state B through path I and II as shown in figure. The change in internal energy is ΔU₁ and ΔU₂ respectively. Then :

• ΔU₁ > ΔU₂

• ΔU₁ < ΔU₂

• ΔU₁ = ΔU₂

• ΔU₁ = ΔU₂ = 0

Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field through both coils, if the same current is flown :

• 1 : $\sqrt{2}$

• 1 : 2

• 2 : 1

• $\sqrt{3}$ : 1

A coil having N turns carries a current as shown in the figure. The magnetic field intensity at point P is :

• $\frac{{\mathrm{\mu }}_0{\mathrm{NiR}}^2}{2({\mathrm{R}}^2 + {\mathrm{x}}^2{)}^{3/2}}$

• $\frac{{\mathrm{\mu }}_0\mathrm{Ni}}{2\mathrm{R}}$

• $\frac{{\mathrm{\mu }}_0{\mathrm{NiR}}^2}{(\mathrm{R} + \mathrm{x}{)}^2}$

• zero