Dimension – JEE Main Study Material

Question

Asked in: JEE Main 2016-2016

A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD = C ln(BD) holds true. Then which of the combination is not a meaningful quantity?

A.	$A^{2}-B^{2}C^{2}$
B.	$\frac{\left ( A-C \right )}{D}$
C.	$\frac{A}{B}-C$
D.	$\frac{C}{BD}-\frac{(AD)^2}{C}$

Question

Asked in: BITSAT-2018

Which one of the following represents the correct dimensions of the coefficient of viscosity?

A.	ML^-1T^-2
B.	MLT^-1
C.	ML^-1T ^-1
D.	ML^-2T^-2

Question

Choose the correct statement about Dimension

A.	It is used to express only the fundamental quantity
B.	It is used to represent only Derived quantity
C.	It is defined as the power to which fundamental quantities must be raised in order to express the given physical quantities.
D.	None of these

Question

What is the dimension of Mass?

A.	[M]
B.	[L]
C.	[T]
D.	[K]

Question

Asked in: JEE Main 2022-2022

Identify the pair of physical quantities that 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

Question

Asked in: JEE Main 2022-2022

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

Question

Asked in: JEE Main 2022-2022

The $\mathrm{SI}$ unit of a physical quantity is pascal-second. The dimensional formula of this quantification will be :

A.	$\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]$
B.	$\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
C.	$\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]$
D.	$\left[\mathrm{M^{-1}L}^{3} \mathrm{~T}^{0}\right]$

Question

Asked in: JEE Main 2022-2022

Which of the following physical quantities have the same dimensions?

A.	Electric displacement $(\overrightarrow{\mathrm{D}})$ and surface charge density
B.	Displacement current and electric field
C.	Current density and surface charge density
D.	Electric potential and energy

Question

Asked in: JEE Main 2022-2022

The dimensions $\left(\frac{\mathrm{B}^2}{\mu_0}\right)_{\text { }}$ will be: (if $\mu_0$ : permeability of free space and B : magnetic field)

A.	$\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
B.	$\left[\mathrm{MLT}^{-2}\right]$
C.	$\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
D.	$\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]$

Question

Asked in: JEE Main 2021-2021

Match List I with List II.

List-I	List-II
(a) Capacitance, C	$(i) \mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}$
(b) Permittivity of free space, $\varepsilon _{0}$	$(ii) \mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{4} \mathrm{~A}^{2}$
(c) Permeability of free space, $\mu _{0}$	$(iii) \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}$
(d) Electric field, E	$(iv) \mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2} \mathrm{~A}^{-2}$

Choose the correct answer from the options given below

A.	$\left[\varepsilon_0\right]=\left[M^{-1} L^{-3} T^4 A^2\right]$
B.	Permeability of free space, $\mu_0$ & $\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^4 \mathrm{~A}^2$
C.	Capacitance, C -$\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-3} \mathrm{~A}^{-1}$
D.	Electric field, E -$\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}$

Question

Asked in: JEE Main 2021-2021

If E, L, M, and G denote the quantities as energy, angular momentum, mass, and constant of gravitation respectively, then the dimensions of P in the formula $P= EL^{2}M^{-5}G^{-2}$ are:

A.	$\left [ M^{1}L^{1}T^{-2} \right ]$
B.	$\left [ M^{0}L^{1}T^{0}\right ]$
C.	$\left [ M^{-1}L^{-1}T^{2}\right ]$
D.	$\left [ M^{0}L^{0}T^{0}\right ]$

Question

Asked in: JEE Main 2021-2021

Match List - I with List - II.

List - I	List - II
(a) Torque	(i) $\mathrm{MLT}^{-1}$
(b) Impulse	(ii) $\mathrm{MT}^{-2}$
(c) Tension	(iii) $\mathrm{ML}^2 \mathrm{~T}^{-2}$
(d) Surface Tension	(iv) $\mathrm{MLT}^{-2}$

Choose the most appropriate answer from the option given below :

A.	(a) - (iii), (b) - (iv), (c) - (i), (d) - (ii)
B.	(a) - (iii), (b) - (i), (c) - (iv), (d) - (ii)
C.	(a) - (i), (b) - (iii), (c) - (iv), (d) - (ii)
D.	(a) - (ii), (b) - (i), (c) - (iv), (d) - (iii)

Question

The dimensions of the coefficient of viscosity can be represented by:

A.	$[ML^{-1}T^{-2}]$
B.	$[MLT^{-1}]$
C.	$[ML^{-1}T^{-1}]$
D.	$[M^{-1}L^{-1}T^{-1}]$

Question

Asked in: JEE Main-2024

The dimensional formula of angular impulse is:

A.	$\left[\mathrm{ML}^{-2} \mathrm{~T}^{-1}\right]$
B.	$\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
C.	$\left[\mathrm{MLT}^{-1}\right]$
D.	$\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$

Question

If viscous force F depends on viscosity 'n', velocity of sphere 'v' and radius r as

F= K n^x r^y v^z

, where K is the dimensionless constant. Then the value of x, y and z is :

A.	x=2, y=0, z=1
B.	x=2, y=1, z=1
C.	x=1, y=1, z=1
D.	x=0, y=2, z=1

Question

Select the pair whose dimension are same:

A.	Stress and strain
B.	Power and force
C.	Surface tension and surface energy
D.	Pressure and force

Question

The dimension of the dielectric constant is :

A.	M¹L¹T⁰
B.	M⁰L¹T¹
C.	M⁰L⁰T¹
D.	M⁰L⁰T⁰

Question

The dimension of Rydberg constant is -

A.	M⁰L^-1T^-1
B.	M¹L⁰T^-1
C.	M⁰L^-1T¹
D.	M⁰L^-1T⁰

Question

The dimensional formula for gravitational constant G is -

A.	$\left[M^1 L^2 T^{-3}\right]$
B.	$\left[M^1 L^{-2} T^{-3}\right]$
C.	$\left[M^{-1} L^3 T^{-2}\right]$
D.	$\left[M^1 L^{-3} T^{-2}\right]$

Question

The unit of specific resistance is :

A.	Ohm/Metre
B.	Ohm/Metre²
C.	Ohm-Metre
D.	(Ohm-Metre)^-1

Question

Direction: In the following question, a statement of Assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion: Light year is a unit of distance but year is a unit of time.

Reason: Light year is the time taken by the light to reach the earth from the sun.

A.	If both assertion and reason are true and reason is the correct explanation of assertion.
B.	If both assertion and reason are true but reason is not the correct explanation of assertion.
C.	If assertion is true but reason is false.
D.	If both assertion and reason are false.

Question

Asked in: JEE Main-2024

If $\mathrm{G}$ be the gravitational constant and $\mathrm{u}$ be the energy density then which of the following quantity have the dimension as that the $\sqrt{\mathrm{uG}}$ :

A.	Pressure gradient per unit mass
B.	Force per unit mass
C.	Gravitational potential
D.	Energy per unit mass

Question

On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct:

A.	$y=a \sin \frac{2 \pi t}{T}$
B.	$y=a \sin \omega t$
C.	$y=\frac{a}{T} \sin \left(\frac{t}{a}\right)$
D.	$y=a \sqrt{2}\left[\sin \left(\frac{2 \pi t}{t}\right)-\cos \left(\frac{2 \pi t}{T}\right)\right]$

Question

Asked in: JEE Main-2024

Match List I with List II

	LIST I		LIST II
A.	Torque	I.	$\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]$
B.	Magnetic field	II.	$\left[\mathrm{L}^2 \mathrm{~A}^1\right]$
C.	Magnetic moment	III.	$\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]$
D.	Permeability of free space	IV.	$\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$

Choose the correct answer from the options given below:

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

Question

Asked in: JEE Main-2023

Match List I with List II:

Choose the correct answer from the options given below:

A.	A-II, B – III, C-I, D-IV
B.	A-II, B – III, C-IV, D-I
C.	A-III, B – II, C-IV, D-I
D.	A-III, B – II, C-I, D-IV

Question

[M⁰ L²T^-2] is the dimension of :

A.	Latent heat
B.	Gravitational potential
C.	Both a and b
D.	Energy gradient

Question

$\left[M^1 L^0 T^{-2} A^{-1}\right]$ is dimension formula for -

A.	Magnetic flux
B.	Specific resistance
C.	Magnetic induction
D.	Capacitance

Question

For any physical quantity Q numerical value n is related to unit u by the relation-

A.	$\ n \alpha u^2$
B.	$n \alpha u$
C.	$n \alpha \sqrt{u}$
D.	$\operatorname{n} \alpha \frac{1}{u}$

Question

The dimension of the permittivity of free space is

A.	$M^{-3} L^{-1} T^4 A^2$
B.	$M L T^4$
C.	$M^{-1} L^{-3} T^4 A^2$
D.	$M L^3 T^{-3} A^{-2}$

Question

Asked in: BITSAT-2018

Dimensions of relative density is

A.	kg/m $^{3}$
B.	$\left[M L^{-3}\right]$
C.	Dimensionless
D.	$\left[M^2 L^{-6}\right]$

Question

Given that $\int e^{a x} d x=a^{-2 m} e^{a x}+C$ then find out the value of $m$ (Dimension of $x=L^1$ ).

A.	00.50
B.	-
C.	-
D.	-

Question

Asked in: JEE Main-2025

The expression given below shows the variation of velocity (v) with time (t),

$v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}$

The dimension of, $\mathrm{ABC}$ is :

A.	$\left[\mathrm{M}^0 \mathrm{L}^1 \mathrm{~T}^{-3}\right]$
B.	$\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-3}\right]$
C.	$\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^{-2}\right]$
D.	$\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$

Question

Asked in: JEE Main-2025

Match List I with List II.

List-I		List-II
A	Young’s Modulus	I	$\mathrm{ML}^{-1} \mathrm{~T}^{-1}$
B	Torque	II	$\mathrm{ML}^{-1} \mathrm{~T}^{-2}$
C	Coefficient of Viscosity	III	$\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}$
D	Gravitational Constant	IV	$\mathrm{ML}^2 \mathrm{~T}^{-2}$

Choose the correct answer from the options given below:

A.	(A)-(I), (B)-(III), (C)-(II), (D)-(IV)
B.	(A)-(II), (B)-(I), (C)-(IV), (D)- (III)
C.	(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
D.	(A)-(II), (B)-(IV), (C)-(I), (D)-(III)

Question

Asked in: JEE Main-2025

The equation for real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where $\mathrm{P}, \mathrm{V}, \mathrm{T}$ and R are the pressure, volume, temperature and gas constant, respectively. The dimension of $\mathrm{ab}^{-2}$ is equivalent to that of:

A.	Planck's constant
B.	Compressibility
C.	Strain
D.	Energy density

Question

Asked in: JEE Main-2025

If $\mu_0$ and $\varepsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0 \varepsilon_0}\right)$ is :

A.	$\mathrm{L} / \mathrm{T}^2$
B.	$L^2 / T^2$
C.	$\mathrm{T}^2 / \mathrm{L}$
D.	$T^2 / L^2$

Question

Asked in: JEE Main-2025

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Gravitational constant	I.	$\left[\mathrm{LT}^{-2}\right]$
B.	Gravitational potential energy	II.	$\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]$
C.	Gravitational potential	III.	$\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
D.	Acceleration due to gravity	IV.	$\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{-2}\right]$

Choose the correct answer from the options given below :

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

Question

Asked in: JEE Main-2025

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Boltzmann constant	I.	$\mathrm{ML}^2 \mathrm{~T}^{-1}$
B.	Coefficient of viscosity	II.	$\mathrm{MLT}^{-3} \mathrm{~K}^{-1}$
C.	Planck's constant	III.	$\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}$
D.	Thermal conductivity	IV.	$\mathrm{ML}^{-1} \mathrm{~T}^{-1}$

Choose the correct answer from the options given below :

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

Question

Asked in: JEE Main-2025

The dimension of $\sqrt{\frac{\mu_0}{\epsilon_0}}$ is equal to that of :
( $\mu_0=$ Vacuum permeability and $\epsilon_0=$ Vacuum permittivity)

A.	Voltage
B.	Capacitance
C.	Inductance
D.	Resistance

Question

Asked in: JEE Main-2025

Match List-I with List-II.

	List-I		List-II
(A)	Mass density	(I)	$\left[\mathrm{ML}^2 \mathrm{~T}^{-3}\right]$
(B)	Impulse	(II)	$\left[\mathrm{MLT}^{-1}\right]$
(C)	Power	(III)	$\left[\mathrm{ML}^2 \mathrm{~T}^0\right]$
(D)	Moment of inertia	(IV)	$\left[\mathrm{ML}^{-3} \mathrm{~T}^0\right]$

Choose the correct answer from the options given below :

A.	(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
B.	(A)-(I), (B)-(III), (C)-(IV), (D)-(II)
C.	(A)-(IV), (B)-(II), (C)-(I), (D)-(III)
D.	(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

Question

Asked in: JEE Main-2025

The unit of $\sqrt{\frac{2 I}{\epsilon_0 c}}$ is :
( $\mathrm{I}=$ intensity of an electromagnetic wave, $\mathrm{c}:$ speed of light)

A.	Vm
B.	NC
C.	Nm
D.	$\mathrm{NC}^{-1}$

Exam	Chapter
JEE MAIN	Physics and Measurement

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Dimension - (Concept)

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