Dimension of a Physical Quantity Match List-I with List-II 01

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Q.
Match List-I with List-II: [2024]

List I List II

A Torque (I) $[M^{1} L^{2} T^{- 2} A^{- 2}]$

B Magnetic Field (II) $[L^{2} A^{1}]$

C Magnetic moment (III) $[M^{1} T^{- 2} A^{- 1}]$

D Permeability of free space (IV) $[M^{1} L^{2} T^{- 2}]$

Choose the correct answer from the options given below:

1 A-III, B-l, C-II, D-IV

2 A-IV, B-II, C-III, D-I

3 A-IV, B-III, C-II, D-I

4 A-I, B-III, C-II, D-IV

Ans.
(3)

   $[\vec{τ}] = [\vec{r} \times \vec{F}] = [M L^{2} T^{- 2}]$

   $[B] = [\frac{M L T^{- 2}}{A T L T^{- 1}}] = [M A^{- 1} T^{- 2}]$

   $[M] = [I \times A] = [A L^{2}]$

   $B = \frac{μ_{0}}{4 π} \frac{I d l \sin θ}{r^{2}} \Rightarrow [μ] = [\frac{B r^{2}}{I d l}]$

   $\Rightarrow [μ] = [\frac{M T^{- 2} A^{- 1} \times L^{2}}{A L}] = [M L T^{- 2} A^{- 2}]$

Solution

1 A-III, B-l, C-II, D-IV

2 A-IV, B-II, C-III, D-I

3 A-IV, B-III, C-II, D-I

4 A-I, B-III, C-II, D-IV

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	List I		List II
A	Torque	(I)	$[M^{1} L^{2} T^{- 2} A^{- 2}]$
B	Magnetic Field	(II)	$[L^{2} A^{1}]$
C	Magnetic moment	(III)	$[M^{1} T^{- 2} A^{- 1}]$
D	Permeability of free space	(IV)	$[M^{1} L^{2} T^{- 2}]$

Solution

Q. Match List-I with List-II: [2024] List I List II A Torque (I) [M1L2T-2A-2] B Magnetic Field (II) [L2A1] C Magnetic moment (III) [M1T-2A-1] D Permeability of free space (IV) [M1L2T-2] Choose the correct answer from the options given below:

1 A-III, B-l, C-II, D-IV

2 A-IV, B-II, C-III, D-I

3 A-IV, B-III, C-II, D-I

4 A-I, B-III, C-II, D-IV

Ans. (3) [τ→]=[r→×F→]=[ML2T-2] [B]=[MLT-2ATLT-1]=[MA-1T-2] [M]=[I×A]=[AL2] B=μ04π Idl sinθr2⇒[μ]=[Br2Idl] ⇒[μ]=[MT-2 A-1×L2AL]=[MLT-2 A-2]

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