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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-m
3. kg-m2-s 
4. kg-m2/s 

Subtopic:  Dimensions |
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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. \(\dfrac{Fx}{t} ,~ Kx, ~ ht\)
Subtopic:  Dimensions |
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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 |
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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)
Subtopic:  Dimensions |
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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 |
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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 |
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Which of the quantities below have the same dimensions?
(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) \(\dfrac{\text{power}}{\text{area}}\)
1. A, B
2. B, C
3. A, C
4. A, B, C
Subtopic:  Dimensions |
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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. \(\frac{Q}{A}=\frac{k}{\mu}\left(\frac{{\large p}_{1}-{\large p}_{2}}{L}\right) \)
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
Subtopic:  Dimensions |
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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 |
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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. \(\dfrac{\text{charge}}{\text{energy}}\)
Subtopic:  Dimensions |
 69%
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