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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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 |
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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%
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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. \(\dfrac{\text{inductance}}{\text{capacitance}}\)
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%
From NCERT
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Consider the efficiency of Carnot’s engine is given by \(\eta=\dfrac{\alpha \beta}{\sin \theta} \log _{\mathrm{e}} \dfrac{\beta {x}}{\mathrm{kT}}\), where \(\alpha\) and \(\beta\) are constants. If \(T\) is temperature, \(k\) is Boltzman constant, \(\theta\) is angular displacement and \(x\) has the dimensions of length. Then, choose the incorrect option.
| 1. | Dimensions of \(\beta\) are same as that of force. |
| 2. | Dimensions of \(\alpha^{-1}x\) are same as that of energy. |
| 3. | Dimensions of \(\eta^{-1} \sin \theta\) are same as that of \(\alpha \beta\). |
| 4. | Dimensions of \(\alpha\) same as that of \(\beta\). |
Subtopic: Dimensions |
52%
From NCERT
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Hints
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The quantity: \({\mathcal P}=\int|\psi(\vec r)|^2dV,\) is the probability of finding a particle in the given volume. The integration is carried over the given volume. The dimension of \(|\psi(\vec r)|\) is:
1. \(L^{-3}\)
2. \(L^{-3/2}\)
3. \(L^{3/2}\)
4. \(M^0L^0T^0\)
1. \(L^{-3}\)
2. \(L^{-3/2}\)
3. \(L^{3/2}\)
4. \(M^0L^0T^0\)
Subtopic: Dimensions |
56%
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. \(\dfrac{\eta c}{K}\)
1. \(Kc\eta\)
2. \(\Large\frac{Kc}{\eta}\)
3. \(\Large\frac{K\eta}{c}\)
4. \(\dfrac{\eta c}{K}\)
Subtopic: Dimensions |
55%
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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 |
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%
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