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The quantity "Action" (\(S\)) is defined by the equation:
\(S=\int_{0}^{t}(K-U)^{} d t\)
where \(K\) is the kinetic energy, \(U\) is the potential energy and the integral is over the time, \(t\) during the motion.
The proper unit of action will be:
1.
kg-m/s
2.
kg-m2
3.
kg-m2-s
4.
kg-m2/s
Subtopic: Â Dimensions |
 72%
Level 2: 60%+
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The dimension of which group of quantities is the same?
\(h\) : Planck's constant, \(K\) : kinetic energy, \(\omega\) : angular speed/frequency, \(F\): force, \(L\) : inductance, \(i\) : current, \(q\) : charge, \(t\) : time, \(x\): distance
1. \(h, ~Ftx,~ Liq\)
2. \(K , h\omega , \omega Li\)
3. \(Fx, ~Li^2,~K \omega\)
4. \(\dfrac{Fx}{t} ,~ Kx, ~ ht\)
\(h\) : Planck's constant, \(K\) : kinetic energy, \(\omega\) : angular speed/frequency, \(F\): force, \(L\) : inductance, \(i\) : current, \(q\) : charge, \(t\) : time, \(x\): distance
1. \(h, ~Ftx,~ Liq\)
2. \(K , h\omega , \omega Li\)
3. \(Fx, ~Li^2,~K \omega\)
4. \(\dfrac{Fx}{t} ,~ Kx, ~ ht\)
Subtopic: Â Dimensions |
 55%
Level 3: 35%-60%
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Which of the following quantities have the same dimension?
1. B, C
2. A, B, C
3. B, D
4. A, B, C, D
| (A) | \(\dfrac{\text{(Magnetic flux)}^2}{\text{Electrical resistance}}\) | (B) | \(\text{Torque}\times\text{time}\) |
| (C) | \(\text{Momentum}\times\text{length}\) | (D) | \(\dfrac{\text{Power}}{\text{time}}\) |
2. A, B, C
3. B, D
4. A, B, C, D
Subtopic: Â 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: Â Dimensions |
 58%
Level 3: 35%-60%
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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
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: Â 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: Â 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: Â 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: Â 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: Â 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: Â Dimensions |
 69%
Level 2: 60%+
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