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Which of the following quantities have the same dimension?
(A)
\(\dfrac{\text{(Magnetic flux)}^2}{\text{Electrical resistance}}\)
(B)
\(\text{Torque}\times\text{time}\)
(C)
\(\text{Momentum}\times\text{length}\)
(D)
\(\dfrac{\text{Power}}{\text{time}}\)
1. B, C
2. A, B, C
3. B, D
4. A, B, C, D
Subtopic: Dimensions |
Level 3: 35%-60%
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What is the unit of the quantity represented by: \(\dfrac{\text{(Angular momentum)}}{\text{(electric charge)}^2}\)
1. \(\Omega\) (ohm)
2. s/m
3. \(\text{H }\)(henry)
4. \(\text{F }\) (farad)
1. \(\Omega\) (ohm)
2. s/m
3. \(\text{H }\)(henry)
4. \(\text{F }\) (farad)
Subtopic: Dimensions |
58%
Level 3: 35%-60%
Hints
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
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%+
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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%
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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 |
50%
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. | \(\dfrac{\text{inductance}}{\text{capacitance}}\) |
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)
(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%+
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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%+
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