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Dimensionless Quantities - Practice Questions & MCQ

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Permittivity of free space and dielectric constant (k), Magnetic Field ,Permeability of free space, Magnetic flux and self inductance are considered the most difficult concepts.

  • Dimensionless Quantities, Heat, Latent heat , Specific heat capacity and Temperature are considered the most asked concepts.

  • 53 Questions around this concept.

Solve by difficulty

Strain has same dimension as that of:

The unit of absolute permittivity is

Which of the following units denotes the dimensions ML2/Q2,   where Q denotes the electric charge?

The dimension of magnetic field in M, L, T and C (coulomb) is given as:

Concepts Covered - 7

Dimensionless Quantities

The quantities which do not have dimension are known as Dimensionless Quantities.

Because these quantities are the ratio of two similar quantities.

Example.

  1. Strain

  2. Refractive index

  3. Relative density

  4. Poisson's ratio  

So all these quantities are dimensionless.

Or they have a dimensional formula which is equal to .

And all these quantities are unitless.

Heat, Latent heat , Specific heat capacity and Temperature
  1. Temperature-

It is fundamental quantity.

 Dimensional formula- M^{0}L^{0}T^{0}K^{1}(where K represents Kelvin)

 SI unit-  Kelvin

 

  1. Heat

 Dimensional formula-   ML^{2}T^{-2}

 SI unit- Joule

 

  1. Latent heat

Its dimensional formula  is equal to M^{0}L^{2}T^{-2}

And its SI unit  is equal to m^{2}s^{-2}


 

  1. Specific heat capacity 

 Dimensional formula-   M^0L^2T^{-2}K^{-1} 

 SI unit- \frac{Joule}{Kg.K} 

Surface tension, Surface energy

Surface tension- Dimensional formula-M^{1}L^{0}T^{-2}

                             SI unit-  Kgs^{-2}

Surface energy(per unit area) - Dimensional formula-M^{1}L^{0}T^{-2}

                             SI unit-  Kgs^{-2}

But (Surface tension) and (surface energy per unit area) will have the same dimensional formula and SI units.

Vander waals constant (a and b)

 The real gas equation is given as 

\left ( P+\frac{n^{2}a}{V^{2}} \right )\left ( V-nb \right )= nRT

 Where a and b are called Vander wall's constant.

1)  Vander Waal's constant (a)

    Dimension- ML^{5}T^{-2}

     Unit- Newton -m ^{4}

2) Vander waal 's constant (b)

Dimension- M^{0}L^{3}T^{0}

     Unit- m^{3}

Voltage,Resistance and resistivity

1) Voltage (V)

      Dimension-  \dpi{100} ML^{2}T^{-3}A^{-1}

      Unit-  Volt

2) Resistance (R)

      Dimension-  ML^{2}T^{-3}A^{-2}

      Unit- Ohm

3) Resistivity (\rho)

      Dimension-  ML^{3}T^{-3}A^{-2}

      Unit-   Ohm - metre

Permittivity of free space and dielectric constant (k)

1) The permittivity of free space( \epsilon_{o})

    Dimension- \ M^{-1}L^{-3}T^{4}A^{2}

    Unit-   \dpi{100} C^2N^{-1}m^{-2} or Farad/Metre

2) dielectric constant (k)

    Dimension- M^{0}L^{0}T^{0}

    Unit-  Unitless

Magnetic Field ,Permeability of free space, Magnetic flux and self inductance

1) Magnetic Field (B)

     Dimension- M^{1}L^{0}T^{-2}A^{-1}  

     Unit-     \dpi{100} \frac{newton }{ampere - metre } \ \ \ or \ \ \ \ \frac{volt -second }{metre^{2}}

2)Permeability of free space  

The dimension of permeability of free space (\mu_{o})-M^{1}L^{1}T^{-2}A^{-2}  

SI unit- \frac{newton}{ampere^{2}},\frac{henry}{metre}

 

3) Magnetic flux (φ)

     Dimension-  ML^{2}T^{-2}A^{-1}

     Unit-  Weber or   Volt-second

4)  Coefficient of self-induction (L)

      Dimension- ML^{2}T^{-2}A^{-2}

      Unit-  Henry 

Study it with Videos

Dimensionless Quantities
Heat, Latent heat , Specific heat capacity and Temperature
Surface tension, Surface energy

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