1. 27 MV
2. 18 MV
3. 20 MV
4. 23 MV
1. 1.0 m\(\Omega\)
2. 2.0 m\(\Omega\)
3. 3.0 m\(\Omega\)
4. None of these
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. \(x^2_0=s^2_0+\sqrt2x_0s_0~^{1/2}\)
What is the change in the volume of \(1.0~\mathrm{L}\) kerosene when it is subjected to an extra pressure of \(2.0 \times 10^5 \mathrm{~Nm}^{-2}\) from the following data?
(The density of kerosene \(=800~\mathrm{kgm^3}\) and the speed of sound in kerosene \(=1330~\mathrm{ms^{-1}}\))
1. \(
0.97 \mathrm{~cm}^{-3}
\)
2. \( 0.66 \mathrm{~cm}^{-3} \)
3. \(
0.15 \mathrm{~cm}^{-3}
\)
4. \(0.59 \mathrm{~cm}^{-3}\)
Water level is maintained in a cylindrical vessel up to a fixed height \(H.\) The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel, so that the water stream coming out of the hole strikes the horizontal plane of the greatest distance from the vessel?
1. \(h=\frac{H}{2}\)
2. \(h=\frac{3H}{2}\)
3. \(h=\frac{2H}{3}\)
4. \(h=\frac{3}{4}H\)
The figure shows a spring + block + pulley system which is light. The time period of mass would be:
1. \(2\pi\sqrt{\frac{k}{m}}\)
2. \(\frac{1}{2\pi}\sqrt{\frac{k}{m}}\)
3. \(2\pi\sqrt{\frac{m}{k}}\)
4. None of these
A pendant having a bob of mass \(m\) is hanging in a ship sailing along the equator from east to west. When the strip is stationary with respect to water, the tension in the string is \(T_0.\) The difference between \(T_0\) and earth attraction on the bob, is:
1. \(\frac{mg+m\omega^2R}{2}\)
2. \(\frac{m\omega^2R}{3}\)
3. \(\frac{m\omega^2R}{2}\)
4. \(\frac{m\omega^2}R\)