JEE Main Units and Measurements Previous year Question

16.(JEE Main 2022 (Online) 28th July Morning Shift )

The dimensions of $(\frac{B^{2}}{μ_{0}})$ will be :

(if $μ_{0}$ : permeability of free space and $B$ : magnetic field)

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

(B) $[M L T^{- 2}]$

(C) $[M L^{- 1} T^{- 2}]$

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

Correct answer is (C)

$[\frac{B^{2}}{μ_{0}}] =$ [Energy density]

$= \frac{M L^{2} T^{- 2}}{L^{3}} = M L^{- 1} T^{- 2}$

17.(JEE Main 2022 (Online) 27th June Evening Shift )

The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be :

(A) [ML^{$-$ 1}T^{$-$ 1}]

(B) [ML^{$-$ 1}T^{$-$ 2}]

(C) [ML²T^{$-$ 1}]

(D) [M^{$-$ 1}L³T⁰]

Correct answer is (A)

[pascal-second] = $\frac{M L T^{- 2}}{L^{2}} \times T$

$= M L^{- 1} T^{- 1}$

18.(JEE Main 2022 (Online) 26th June Evening Shift )

The dimension of mutual inductance is :

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

(B) $[M L^{2} T^{- 3} A^{- 1}]$

(C) $[M L^{2} T^{- 2} A^{- 2}]$

(D) $[M L^{2} T^{- 3} A^{- 2}]$

Correct answer is (C)

$∵$ $U = \frac{1}{2} M i^{2}$

$\Rightarrow [M] = \frac{[U]}{[i^{2}]} = \frac{M L^{2} T^{- 2}}{A^{2}}$

$= [M L^{2} T^{- 2} A^{- 2}]$

19.(JEE Main 2022 (Online) 24th June Evening Shift )

Identify the pair of physical quantities that have same dimensions:

(A) velocity gradient and decay constant

(B) Wien's constant and Stefan constant

(C) angular frequency and angular momentum

(D) wave number and Avogadro number

Correct answer is (A)

Velocity gradient $= \frac{d v}{d x}$

$\Rightarrow$ Dimensions are $\frac{[L T^{- 1}]}{[L]} = [T^{- 1}]$

Decay constant $λ$ has dimensions of $[T^{- 1}]$ because of the relation $\frac{d N}{d t} = - λ$ N

$\Rightarrow$ Velocity gradient and decay constant have same dimensions.

20.(JEE Main 2022 (Online) 24th June Morning Shift )

Identify the pair of physical quantities which have different dimensions:

(A) Wave number and Rydberg's constant

(B) Stress and Coefficient of elasticity

(C) Coercivity and Magnetisation

(D) Specific heat capacity and Latent heat

Correct answer is (D)

$[S] = \frac{[C]}{[m] \times [Δ T]}$

and, $[L] = \frac{[Q]}{[m]}$

$\Rightarrow$ They have different dimensions.