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The quantity \(\eta\) is defined by: \(\eta=\dfrac{1}{\mu_0\sigma}\)
where \(\mu_0\) is the permeability of free space and \(\sigma\) is the electrical conductivity (of a plasma). \(\eta\) is referred to as the magnetic diffusivity. Its SI unit is:
1. m2/s
2. m/s2
3. C-m2/s
4. T-m/s
Subtopic: Dimensions |
Level 3: 35%-60%
Hints
Which of the following, is dimensionless?
| 1. | \(\dfrac{\text{pressure}}{\text{density}\times\text{acceleration}}\) | 2. | \(\dfrac{\text{density}\times\text{pressure}}{\text{speed}}\) |
| 3. | \(\dfrac{\text{viscosity}\times\text{speed}}{\text{surface tension}}\) | 4. | \(\dfrac{\text{surface tension}}{\text{(speed)}^2}\) |
Subtopic: Dimensions |
80%
Level 1: 80%+
Hints
Which of the quantities below have the same dimensions?
1. A, B
2. B, C
3. A, C
4. A, B, C
| (A) | \(\dfrac{\text{electric field }\times\text{ magnetic field}}{\mu_0}\) |
| (B) | \(\dfrac{\varepsilon_0\times\text{(electric potential)}^2\times\text{ velocity}}{\text{area}}\) |
| (C) | \(\dfrac{\text{power}}{\text{area}}\) |
2. B, C
3. A, C
4. A, B, C
Subtopic: Dimensions |
Level 3: 35%-60%
Hints
Darcy's law describes the volume flow rate \((Q) \) of a viscous fluid (viscosity : \(\mu\)) through a porous medium, under the action of a pressure difference. \(\dfrac{Q}{A}=\dfrac{k}{\mu}\left(\dfrac{{\large p}_{1}-{\large p}_{2}}{L}\right) \)
Here, \(k\) is the permeability of the medium. The unit of \(k\) is (SI units):
1. m
2. m2
3. m2/s
4. m/s2
Here, \(k\) is the permeability of the medium. The unit of \(k\) is (SI units):
1. m
2. m2
3. m2/s
4. m/s2
Subtopic: Dimensions |
Level 3: 35%-60%
Hints
Which, of the following, is dimensionless?
1. \(\text{impedance}\times\text{conductance} \)
2. \(\dfrac{\text{emissive power}}{\text{emissivity}}\)
3. \(\dfrac{\text{electric field}}{\text{magnetic field}}\)
4. \(\dfrac{\text{inductance}}{\text{capacitance}}\)
1. \(\text{impedance}\times\text{conductance} \)
2. \(\dfrac{\text{emissive power}}{\text{emissivity}}\)
3. \(\dfrac{\text{electric field}}{\text{magnetic field}}\)
4. \(\dfrac{\text{inductance}}{\text{capacitance}}\)
Subtopic: Dimensions |
Level 3: 35%-60%
Hints
Find the dimension of the quantity \(\varepsilon_0hc\):
(where \(\varepsilon_0=\) permittivity of free space, \(h=\) Planck's constant, and \(c=\) speed of light in vacuum)
1. \(\text{(charge)}\times\text{(energy)}\)
2. \(\text{(energy)}^2\)
3. \(\text{(charge)}^2\)
4. \(\dfrac{\text{charge}}{\text{energy}}\)
(where \(\varepsilon_0=\) permittivity of free space, \(h=\) Planck's constant, and \(c=\) speed of light in vacuum)
1. \(\text{(charge)}\times\text{(energy)}\)
2. \(\text{(energy)}^2\)
3. \(\text{(charge)}^2\)
4. \(\dfrac{\text{charge}}{\text{energy}}\)
Subtopic: Dimensions |
69%
Level 2: 60%+
Hints
The dimensions of the elastic modulus of a material are the same as:
1. torque
2. surface tension
3. angular momentum
4. pressure
1. torque
2. surface tension
3. angular momentum
4. pressure
Subtopic: Dimensions |
81%
Level 1: 80%+
Hints
Match the units mentioned in List-I with the units in List-II.
| List-I | List-II | ||
| (a) | H/s | (i) | s2 |
| (b) | H×A | (ii) | Wb |
| (c) | H×F | (iii) | s |
| (d) | \(\Omega\)×F | (iv) | \(\Omega\) |
| 1. | (a)–(ii), (b)–(iv), (c)–(i), (d)–(iii) |
| 2. | (a)–(iv), (b)–(ii), (c)–(i), (d)–(iii) |
| 3. | (a)–(iv), (b)–(ii), (c)–(iii), (d)–(i) |
| 4. | (a)–(ii), (b)–(iii), (c)–(iv), (d)–(i) |
Subtopic: Dimensions |
62%
Level 2: 60%+
Hints
Match the following quantities in List-I with their dimensions in List-II.
| List-I | List-II | ||
| (a) | acceleration | (i) | \([M^0L^0T^0 ]\) |
| (b) | torque | (ii) | \([ML^{-1}T^{-2} ]\) |
| (c) | absorptive power | (iii) | \([LT^{-2} ]\) |
| (d) | pressure | (iv) | \([ML^2T^{-2} ]\) |
| 1. | (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii) |
| 2. | (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv) |
| 3. | (a)-(iii), (b)-(i), (c)-(ii), (d)-(iv) |
| 4. | (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i) |
Subtopic: Dimensions |
86%
Level 1: 80%+
Hints
Match the units of some physical quantities in List-I with their corresponding dimensions in List-II.
| List-I | List-II | ||
| (a) | Ohm | (i) | \([ML^2T^{-2}A^{-1}]\) |
| (b) | Farad | (ii) | \([ML^2T^{-2}A^{-2}]\) |
| (c) | Henry | (iii) | \([M^{-1}L^{-2}T^4A^2]\) |
| (d) | Weber | (iv) | \([ML^2T^{-3}A^{-2}]\) |
| 1. | (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) |
| 2. | (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii) |
| 3. | (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv) |
| 4. | (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i) |
Subtopic: Dimensions |
64%
Level 2: 60%+
Hints
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