If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as $\left[{\mathrm{\eta }}^{\mathrm{x}}{\mathrm{\rho }}^{\mathrm{y}}{\mathrm{r}}^{\mathrm{z}}\right]$, where  are the coefficient of viscosity of the liquid, the density of liquid and radius of the tube respectively, then the values of x, y and z, respectively, will be

1. 1, -1, -1

2. -1, -1, 1

3. -1, -1, -1

4. 1, 1, 1,

Subtopic:  Dimensions |
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If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:
1. [Ev-2T-1]
2. [Ev-1T-2]
3. [Ev-2T-2]
4. [E-2v-1T-3]

Subtopic:  Dimensions |
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If force (F), velocity (v) and time (T) are taken as fundamental units, the dimensions of mass will be

1. [FvT-1]

2. [FvT-2]

3. [Fv-1T-1]

4. [Fv-1T]

Subtopic:  Dimensions |
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The dimensions of ${\left({\mu }_{0}{\epsilon }_{0}\right)}^{-1/2}$ are -

1.

2.

3.

4.

Subtopic:  Dimensions |
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The dimensions of ${\left({\mathrm{\mu }}_{0}{\mathrm{\epsilon }}_{0}\right)}^{-1/2}$ are

1.

2.  $\left[{\mathrm{LT}}^{-1}\right]$

3.

4.

Subtopic:  Dimensions |
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The density of a material in CGS system of units is 4 g/cm3. In a system of units in which unit of length is 10 cm and unit of mass is 100g, the value of density of material will be
1. 0.04
2. 0.4
3. 40
4. 400

Subtopic:  Dimensions |
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The dimensions of $\frac{1}{2}{\mathrm{\epsilon }}_{0}{\mathrm{E}}^{2}$ where ${\epsilon }_{0}$ is the permittivity of free space and E is the electric field, are:

1. [ML2T-2]

2. [ML-1T-2]

3.  [ML2T-1]

4.  [MLT-1]

Subtopic:  Dimensions |
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If the dimensions of a physical quantity are given by MaLbTc, then the physical quantity will be:
1. Pressure if a = 1, b = -1, c = - 2
2. Velocity if a = 1, b = 0, c = - 1
3. Acceleration if a = 1, b = 1, c = - 2
4. Force if a = 0, b =-1, c = - 2
Subtopic:  Dimensions |
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Which two of the following five physical parameters have the same dimensions?
(1) Energy density
(2) Refractive index
(3) Dielectric constant
(4) Young's modulus
(5) Magnetic field

1.  (2) and (4)

2.  (3) and (5)

3.  (1) and (4)

4.  (1) and (5)

Subtopic:  Dimensions |
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Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, length L, time T and current I, would be:

1. $\left[{\mathrm{ML}}^{2}{\mathrm{T}}^{-3}{\mathrm{I}}^{-1}\right]$

2. $\left[{\mathrm{ML}}^{2}{\mathrm{T}}^{-2}\right]$

3. $\left[{\mathrm{ML}}^{2}{\mathrm{T}}^{-1}{\mathrm{I}}^{-1}\right]$

4. $\left[{\mathrm{ML}}^{2}{\mathrm{T}}^{-3}{\mathrm{I}}^{-2}\right]$

Subtopic:  Dimensions |
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