Q. No.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: Dimensions |
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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 |
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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 |
51%
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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
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%
From NCERT
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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: Dimensions |
50%
From NCERT
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The quantities \(K,c,\eta\) represent the thermal conductivity, the specific heat capacity and the viscosity of a liquid. Which, of the following, is dimensionless?
| 1. | \(Kc\eta\) | 2. | \(\Large\frac{Kc}{\eta}\) |
| 3. | \(\Large\frac{K\eta}{c}\) | 4. | \(\Large\frac{\eta c}{K}\) |
Subtopic: Dimensions |
56%
From NCERT
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The diffusion equation is given by:
\(\dfrac{\partial n}{\partial t}=D\dfrac{\partial^2 n}{\partial x^2}\)
where \(n(x,t)\) is the concentration of particles per unit volume at position \(x\), at time \(t\). The dimensions of the diffusion constant \(D,\) are:
1. \(LT^{-1}\)
2. \(L^{-1}T\)
3. \(L^{5}T^{-1}\)
4. \(L^{2}T^{-1}\)
\(\dfrac{\partial n}{\partial t}=D\dfrac{\partial^2 n}{\partial x^2}\)
where \(n(x,t)\) is the concentration of particles per unit volume at position \(x\), at time \(t\). The dimensions of the diffusion constant \(D,\) are:
1. \(LT^{-1}\)
2. \(L^{-1}T\)
3. \(L^{5}T^{-1}\)
4. \(L^{2}T^{-1}\)
Subtopic: Dimensions |
56%
From NCERT
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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%
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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: Dimensions |
57%
From NCERT
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The acceleration due to gravity on the surface of the earth is \(g=10\) m/s2. The value in km/(minute)2 is:
| 1. | \(36\) | 2. | \(0.6\) |
| 3. | \(\dfrac{10}{6}\) | 4. | \(3.6\) |
Subtopic: Dimensions |
61%
From NCERT
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