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Physical Quantities

The dimension...

Question

The dimensional formula of $\frac{1}{2} μ_{0} H^{2}$ ( $μ_{0}$ - Permeability of free space and H-magnetic field intensity) is:

A

M L T^{- 1}

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B

M L^{2} T^{- 2}

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C

M L^{- 1} T^{- 2}

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D

M L^{2} T^{- 1}

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Solution

The correct option is C $M L^{- 1} T^{- 2}$
The given expression is the expression for energy density of a magnetic field. Hence its dimensions must be same as that of energy density, i.e., $[\frac{M L^{2} T^{- 2}}{L^{3}}] = [M L^{- 1} T^{- 2}]$

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Q. Match the following physical quantities with their respective dimensional formula:

(a) Angular Momentum	(e) $[{M L}^{2} T^{- 3}]$
(b) Impulse	(f) $[{M L}^{2} T^{- 1}]$
(c) Pressure	(g) $[M L T^{- 1}]$
(d) Power	(h) $[{M L}^{- 1} T^{- 2}]$

Q. Names of units of some physical quantities are given in List - I and their dimensional formulae are given in List - II. Match the correct pair of the lists.

List - I	List - II
a) Pa-s	e) $[L^{2} T^{- 2} K^{- 1}]$
b) ${N m K}^{- 1}$	f) ${M L T}^{- 3} K^{- 1}$
c) ${J k g}^{- 1} k^{- 1}$	g) ${M L}^{- 1} T^{- 1}$
d) ${W m}^{- 1} k^{- 1}$	h) $[{M L}^{2} T^{- 2} K^{- 1}]$

Q. Some physical constants are given in List - I and their dimensional formulae are given in List - II. Match the following :

List - I	List - II
A) Planck's constant	e) $[{M L}^{- 1} T^{- 2}]$
B) Gravitational constant	f) $[{M L}^{1} T^{- 1}]$
C) Bulk modulus	g) $[{M L}^{2} T^{- 1}]$
D) Linear momentum	h) $[M^{- 1} L^{3} T^{- 2}]$

Q. Match the physical quantities given in Column I with suitable dimensions expressed in Column II.

Column I	Column II
a) Angular momentum	1) $M^{- 1} L^{3} T^{- 2}$
b) Torque	2) ${M L T}^{- 2}$
c) Gravitational constant	3) ${M L}^{2} T^{- 2}$
d) Tension	4) ${M L}^{2} T^{- 1}$

Q. The dimensions of quantity

\frac{1}{μ_{0}} (\to E \times \to B)

[μ_{0} =

permeability of free space,

E^{1} =

electric field strength,

B^{1} =

magnetic field induction

]

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