The rms speed (in m/s) of oxygen molecules of the gas at temperature \(300\) K, is:
1. \(483\)
2. \(504\)
3. \(377\)
4. \(346\)

A horizontal tube of length \(l\) dosed at both ends contains an ideal gas of molecular weight \(M.\) The tube is rotated at a constant angular velocity \(\omega\) about a vertical axis passing through an end. Assuming the temperature to be uniform and constant. If \(P_1\) and \(P_2\) denote the pressure at the free and the fixed end respectively, then choose the correct relation.
1. \(\frac{P_2}{P_1}=e^{\frac{M\omega^2l^2}{2RT}}\)
2. \(\frac{P_1}{P_2}=e^{\frac{M\omega^2}{RT}}\)
3. \(\frac{P_1}{P_2}=e^{\frac{\omega lM}{3RT}}\)
4. \(\frac{P_2}{P_1}=e^{\frac{M^2\omega^2l^2}{3RT}}\)

The parts of two concentric circular arcs joined by two radial lines and carries current \(i.\) The arcs subtend an angle \(\theta\) at the centre of the circle the magnetic field at the centre \(O,\) is:
1. \(\frac{\mu_{_0}i(b-a)\theta}{4\pi ab}\)
2. \(\frac{\mu_{_0}i(b-a)}{4\pi ab}\)
3. \(\frac{\mu_{_0}i(b-a)\theta}{\pi ab}\)
4. \(\frac{\mu_{_0}i(a-b)}{2\pi ab}\)

A particle is subjected to two simple harmonic motions along the X-axis while the other is along a line making an angle of 45° with the X-axis. The two motions are given by \(x = x_0\) sin \(\omega t\) and \(s = s_0\) sin \(\omega t\). The amplitude of the resultant motion is:
1. \(x_0+s_0+2x_0s_0\)
2. \(\sqrt{x^2_0+s^2_0}\)
3. \(\sqrt{x^2_0+s^2_0+2x_0s_0}\)
4. \(x^2_0=s^2_0+\sqrt2x_0s_0~^{1/2}\)