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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Q8:

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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Q9:

What is the unit of the quantity represented by:

\frac{(Angular momentum)}{{(electric charge)}^{2}}

$\dfrac{\text{(Angular momentum)}}{\text{(electric charge)}^2}$

1.

Ω

$\Omega$ (ohm)
2. s/m
3.

H

$\text{H }$ (henry)
4.

F

$\text{F }$ (farad)

Subtopic: Dimensions |

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Q10:

The quantity

η

$\eta$ is defined by:

η = \frac{1}{μ_{0} σ}

$\eta=\dfrac{1}{\mu_0\sigma}$
where

μ_{0}

$\mu_0$ is the permeability of free space and

σ

$\sigma$ is the electrical conductivity (of a plasma).

η

$\eta$ 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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Q11:

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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Q12:

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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Q13:

Darcy's law describes the volume flow rate

(Q)

$(Q)$ of a viscous fluid (viscosity :

μ

$\mu$ ) through a porous medium, under the action of a pressure difference.

\frac{Q}{A} = \frac{k}{μ} (\frac{p_{1} - p_{2}}{L})

$\frac{Q}{A}=\frac{k}{\mu}\left(\frac{{\large p}_{1}-{\large p}_{2}}{L}\right)$
Here,

k

$k$ is the permeability of the medium. The unit of

k

$k$ is (SI units):

1. m
2. m²
3. m²/s
4. m/s²

Subtopic: Dimensions |

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Q14:

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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Q15:

Find the dimension of the quantity

ε_{0} h c

$\varepsilon_0hc$ :
(where

ε_{0} =

$\varepsilon_0=$ permittivity of free space,

h =

$h=$ Planck's constant, and

c =

$c=$ speed of light in vacuum)
1.

(charge) \times (energy)

$\text{(charge)}\times\text{(energy)}$
2.

{(energy)}^{2}

$\text{(energy)}^2$
3.

{(charge)}^{2}

$\text{(charge)}^2$
4.

\frac{charge}{energy}

$\dfrac{\text{charge}}{\text{energy}}$

Subtopic: Dimensions |

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Q16:

The dimensions of the elastic modulus of a material are the same as:
1. torque
2. surface tension
3. angular momentum
4. pressure

Subtopic: Dimensions |

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