Polar molecules are the molecules:
| 1. | that acquires a dipole moment only when the magnetic field is absent. |
| 2. | has a permanent electric dipole moment. |
| 3. | has zero dipole moment. |
| 4. | that acquire a dipole moment only in the presence of an electric field due to displacement of charges. |
| 1. | \(\frac{S}{2},\frac{\sqrt{3gS}}{2}\) | 2. | \(\frac{S}{4}, \sqrt{\frac{3gS}{2}}\) |
| 3. | \(\frac{S}{4},\frac{3gS}{2}\) | 4. | \(\frac{S}{4},\frac{\sqrt{3gS}}{3}\) |
Match Column I and Column II with appropriate relations.
| Column I | Column II | ||
| (A) | Drift Velocity | (P) | \(\dfrac{ \mathrm{m}}{\mathrm{ne}^2 \rho}\) |
| (B) | Electrical Resistivity | (Q) | \(nev_d\) |
| (C) | Relaxation Period | (R) | \(\dfrac{ \mathrm{eE}}{\mathrm{m}} \tau\) |
| (D) | Current Density | (S) | \(\dfrac{E}{J}\) |
| (A) | (B) | (C) | (D) | |
| 1. | (R) | (P) | (S) | (Q) |
| 2. | (R) | (Q) | (S) | (P) |
| 3. | (R) | (S) | (P) | (Q) |
| 4. | (R) | (S) | (Q) | (P) |
If force \([F]\), acceleration \([A]\) and time \([T]\) are chosen as the fundamental physical quantities, then find the dimensions of energy:
1. \(\left[FAT^{-1}\right]\)
2. \(\left[FA^{-1}T\right]\)
3. \(\left[FAT\right]\)
4. \(\left[FAT^{2}\right]\)
The escape velocity from the Earth's surface is \(v\). The escape velocity from the surface of another planet having a radius, four times that of Earth and the same mass density is:
| 1. | \(3v\) | 2. | \(4v\) |
| 3. | \(v\) | 4. | \(2v\) |
A small block slides down on a smooth inclined plane starting from rest at time \(t=0.\) Let \(S_n\) be the distance traveled by the block in the interval \(t=n-1\) to \(t=n.\) Then the ratio \(\dfrac{S_n}{S_{n +1}}\) is:
| 1. | \(\dfrac{2n+1}{2n-1}\) | 2. | \(\dfrac{2n}{2n-1}\) |
| 3. | \(\dfrac{2n-1}{2n}\) | 4. | \(\dfrac{2n-1}{2n+1}\) |
The velocity of a small ball of mass \(M\) and density \(d\), when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \(d\over 2\) then the viscous force acting on the ball will be:
| 1. | \(\frac{3Mg}{2}\) | 2. | \(2Mg\) |
| 3. | \(\frac{Mg}{2}\) | 4. | \(Mg\) |
A thick current-carrying cable of radius '\(R\)' carries current \('I'\) uniformly distributed across its cross-section. The variation of magnetic field \(B(r)\) due to the cable with the distance '\(r\)' from the axis of the cable is represented by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Find the value of the angle of emergence from the prism given below for the incidence ray shown. The refractive index of the glass is \(\sqrt{3}\).
1. \(45^{\circ}\)
2. \(90^{\circ}\)
3. \(60^{\circ}\)
4. \(30^{\circ}\)
A screw gauge gives the following readings when used to measure the diameter of a wire:
Main scale reading: \(0\) mm
Circular scale reading: \(52\) divisions
Given that \(1\) mm on the main scale corresponds to \(100\) divisions on the circular scale, the diameter of the wire that can be inferred from the given data is:
| 1. | \(0.26\) cm | 2. | \(0.052\) cm |
| 3. | \(0.52\) cm | 4. | \(0.026\) cm |
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