A particle moves in the \((x\text-y)\) plane according to the rule \(x = a \sin (\omega t)\) and \(y = a \cos (\omega t)\). The particle follows:
| 1. | a circular path. |
| 2. | a parabolic path. |
| 3. | a straight line path inclined equally to x and y-axes. |
| 4. | an elliptical path. |
The speed of light in media \(M_1\) and \(M_2\) is \(1.5\times10^{8}\) m/s and \(2.0\times10^{8}\) m/s respectively. A ray of light enters from medium \(M_1\) and \(M_2\) at an incidence angle \(i.\) If the ray suffers total internal reflection, the value of \(i\) is:
| 1. | equal to or less than \(\text{sin}^{-1}\left (\frac{3}{5} \right )\) |
| 2. | equal to or greater than \(\text{sin}^{-1}\left (\frac{3}{4} \right )\) |
| 3. | less than \(\text{sin}^{-1}\left (\frac{2}{3} \right )\) |
| 4. | equal to \(\text{sin}^{-1}\left (\frac{2}{3} \right )\) |
A ray of light is incident on a \(60^\circ\) prism at the minimum deviation position. The angle of refraction at the first face (i.e. incident face) of the prism is:
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. zero
A monoatomic gas at pressure P1 and volume V1 is compressed adiabatically to 1/8th its original volume. What is the final pressure of the gas?
1. P1
2. 16 P1
3. 32 P1
4. 64 P1
If \(C_P\) and \(C_V\) denote the specific heats (per unit mass) of an ideal gas of molecular weight \(M\) (where \(R\) is the molar gas constant), the correct relation is:
1. \(C_P-C_V=R\)
2. \(C_P-C_V=\frac{R}{M}\)
3. \(C_P-C_V=MR\)
4. \(C_P-C_V=\frac{R}{M^2}\)
The magnetic moment of a diamagnetic atom is:
1. 1
2. between zero and one
3. equal to zero
4. much greater than one
A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is I, then the resultant magnetic field due to the two semicircular parts at their common centre is:
1.
2.
3.
4.
Two identical bar magnets are fixed with their centres at a distance \(d\) apart. A stationary charge \(Q\) is placed at \(P\) in between the gap of the two magnets at a distance \(D\) from the centre \(O\) as shown in the figure:
The force on the charge \(Q\) is in:
| 1. | direction along \(OP\) |
| 2. | direction along \(PQ\) |
| 3. | direction perpendicular to the plane of the paper |
| 4. | zero |
1. \(1.5\times10^{-3}\) Nm
2. \(1.5\times10^{-2}\) Nm
3. \(3\times10^{-2}\) Nm
4. \(3\times10^{-3}\) Nm
A condenser of capacity C is charged to a potential difference of V1. The plates of the condenser are then connected to an ideal inductor of inductance L. The current through the inductor, when the potential difference across the condenser reduces to V2 is:
1.
2.
3.
4.
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