Dimension of a Physical Quantity

Q 31 :
Match the List I with List II

List I List II

(A) Gravitational constant (I) [ $L T^{- 2}$ ]

(B) Gravitational potential energy (II) [ $L^{2} T^{- 2}$ ]

(C) Gravitational potential (III) [ $M L^{2} T^{- 2}$ ]

(D) Acceleration due to gravity (IV) [ $M^{- 1} L^{3} T^{- 2}$ ]

Choose the correct answer from the options given below: [2025]

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

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4

(1)

(A) $G = \frac{F r^{2}}{m^{2}}$

$[G] = \frac{[M L T^{- 2}] [L^{2}]}{[M^{2}]} = [M^{- 1} L^{3} T^{- 2}] \Rightarrow A \to IV$

(B) P.E. $U = m g h = [M L T^{- 2} L] = [M L^{2} T^{- 2}] \Rightarrow B \to III$

(C) Gravitational Potential, $V = \frac{G M}{r}$

$V = \frac{[M^{- 1} L^{3} T^{- 2}] [M]}{[L]} = [M^{0} L^{2} T^{- 2}] = [L^{2} T^{- 2}] \Rightarrow C \to II$

(D) Acceleration due to gravity $= [g] = [L T^{- 2}] \Rightarrow D \to I$

Q 32 :
Match the List I with List II

List I List II

(A) Boltzmann constant (I) $M L^{2} T^{- 1}$

(B) Coefficient of viscosity (II) $M L T^{- 3} K^{- 1}$

(C) Planck's constant (III) $M L^{2} T^{- 2} K^{- 1}$

(D) Thermal conductivity (IV) $M L^{- 1} T^{- 1}$

Choose the correct answer from the options given below: [2025]

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

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4

(1)

(A) $[k] = \frac{P V}{N T} = \frac{M L^{2} T^{- 2}}{K} = M L^{2} T^{- 2} K^{- 1}$

(B) $[η] = \frac{F}{6 π r v} = \frac{M L T^{- 2}}{L^{2} T^{- 1}} = M L^{- 1} T^{- 1}$

(C) $[h] = \frac{E}{f} = \frac{M L^{2} T^{- 2}}{T^{- 1}} = M L^{2} T^{- 1}$

(D) $\frac{d Q}{d t} = k \frac{A d T}{d x}, k = \frac{(M L^{2} T^{- 3}) L}{L^{2} \cdot K} = M L T^{- 3} K^{- 1}$

Q 33 :
In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^{P} L^{Q} T^{R} A^{S}$ , where value of 'Q' and 'R' are [2025]

(3, –5)
(–2, 2)
(–2, 1)
(1, –1)

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2

3

4

(4)

$\frac{ϕ_{E}}{ϕ_{M}} = \frac{E A}{B A} = \frac{E}{B}$

$\frac{E}{B} = c \Rightarrow [\frac{E}{B}] = [c] = [L T^{- 1}]$

Q 34 :
In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of [ $M^{P} L^{Q} T^{R} A^{S}$ ]. The value of P and Q are: [2025]

–1, 0
–1, 1
1, –1
0, –1

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2

3

4

(4)

Electric dipole moment $(\vec{P}) = q \times 2 l$

Magnetic dipole moment $= (\vec{M}) = I A$

$[\frac{P}{M}] = [\frac{L T A}{L^{2} A}] = L^{- 1} T = M^{0} L^{- 1} T^{1} A^{0}$

After comparing values of P and Q are 0, –1.

Q 35 :
The dimension of $\sqrt{\frac{μ_{0}}{ε_{0}}}$ is equal to that of : ( $μ_{0}$ = Vacuum permeability and $ε_{0}$ = Vacuum permittivity) [2025]

Voltage
Capacitance
Inductance
Resistance

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(4)

$[μ_{0}] = [M L T^{- 2} A^{- 2}]$

$[ε_{0}] = [M^{- 1} L^{- 3} T^{4} A^{2}]$

$[\sqrt{\frac{μ_{0}}{ε_{0}}}] = [M L^{2} T^{- 3} A^{- 2}] ≃ [R]$

Q 36 :
Match the List-I with List-II.

List-I List-II

(A) Mass density (I) $[M L^{2} T^{- 3}]$

(B) Impulse (II) $[M L T^{- 1}]$

(C) Power (III) $[M L^{2} T^{0}]$

(D) Moment of inertia (IV) $[M L^{- 3} T^{0}]$

Choose the correct answer from the options given below : [2025]

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

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(3)

(A) Mass density $= \frac{M}{V} = [M^{1} L^{- 3}]$ ... (IV)

(B) Impulse $= M \times u = [M^{1} L^{1} T^{- 1}]$ ... (II)

(C) Power $= F \cdot v = [M^{1} L^{2} T^{- 3}]$ ... (I)

(D) Moment of inertia $= M r^{2} = [M^{1} L^{2}]$ ... (III)

Q 37 :
In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $[M^{a} L^{b} T^{c}]$ . If b = –3, the value of c is __________. [2025]

0%

(0)

[Modulus of elasticity] $= M L^{- 1} T^{- 2}$

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

[Modulus of elasticity per unit torque] $= \frac{M L^{- 1} T^{- 2}}{M L^{2} T^{- 2}} = L^{- 3}$ .

Topic Question Set

Q 33 :
In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^{P} L^{Q} T^{R} A^{S}$ , where value of 'Q' and 'R' are [2025]

Q 34 :
In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of [ $M^{P} L^{Q} T^{R} A^{S}$ ]. The value of P and Q are: [2025]

Q 35 :
The dimension of $\sqrt{\frac{μ_{0}}{ε_{0}}}$ is equal to that of : ( $μ_{0}$ = Vacuum permeability and $ε_{0}$ = Vacuum permittivity) [2025]

Q 36 :
Match the List-I with List-II.

List-I List-II

(A) Mass density (I) $[M L^{2} T^{- 3}]$

(B) Impulse (II) $[M L T^{- 1}]$

(C) Power (III) $[M L^{2} T^{0}]$

(D) Moment of inertia (IV) $[M L^{- 3} T^{0}]$

Choose the correct answer from the options given below : [2025]

Q 37 :
In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $[M^{a} L^{b} T^{c}]$ . If b = –3, the value of c is __________. [2025]

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	List I		List II
(A)	Gravitational constant	(I)	[ $L T^{- 2}$ ]
(B)	Gravitational potential energy	(II)	[ $L^{2} T^{- 2}$ ]
(C)	Gravitational potential	(III)	[ $M L^{2} T^{- 2}$ ]
(D)	Acceleration due to gravity	(IV)	[ $M^{- 1} L^{3} T^{- 2}$ ]

	List I		List II
(A)	Boltzmann constant	(I)	$M L^{2} T^{- 1}$
(B)	Coefficient of viscosity	(II)	$M L T^{- 3} K^{- 1}$
(C)	Planck's constant	(III)	$M L^{2} T^{- 2} K^{- 1}$
(D)	Thermal conductivity	(IV)	$M L^{- 1} T^{- 1}$

	List-I		List-II
(A)	Mass density	(I)	$[M L^{2} T^{- 3}]$
(B)	Impulse	(II)	$[M L T^{- 1}]$
(C)	Power	(III)	$[M L^{2} T^{0}]$
(D)	Moment of inertia	(IV)	$[M L^{- 3} T^{0}]$

Topic Question Set

Q 32 : Match the List I with List II List I List II (A) Boltzmann constant (I) ML2T–1 (B) Coefficient of viscosity (II) MLT–3K–1 (C) Planck's constant (III) ML2T–2K–1 (D) Thermal conductivity (IV) ML–1T–1 Choose the correct answer from the options given below: [2025]

Q 33 : In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of MPLQTRAS, where value of 'Q' and 'R' are [2025]

Q 34 : In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of [MPLQTRAS]. The value of P and Q are: [2025]

Q 35 : The dimension of μ0ε0 is equal to that of : (μ0 = Vacuum permeability and ε0 = Vacuum permittivity) [2025]

Q 36 : Match the List-I with List-II. List-I List-II (A) Mass density (I) [ML2T-3] (B) Impulse (II) [MLT-1] (C) Power (III) [ML2T0] (D) Moment of inertia (IV) [ML-3T0] Choose the correct answer from the options given below : [2025]

Q 37 : In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of [MaLbTc]. If b = –3, the value of c is __________. [2025]

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Q 33 :
In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^{P} L^{Q} T^{R} A^{S}$ , where value of 'Q' and 'R' are [2025]

Q 34 :
In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of [ $M^{P} L^{Q} T^{R} A^{S}$ ]. The value of P and Q are: [2025]

Q 35 :
The dimension of $\sqrt{\frac{μ_{0}}{ε_{0}}}$ is equal to that of : ( $μ_{0}$ = Vacuum permeability and $ε_{0}$ = Vacuum permittivity) [2025]

Q 36 :
Match the List-I with List-II.

List-I List-II

(A) Mass density (I) $[M L^{2} T^{- 3}]$

(B) Impulse (II) $[M L T^{- 1}]$

(C) Power (III) $[M L^{2} T^{0}]$

(D) Moment of inertia (IV) $[M L^{- 3} T^{0}]$

Choose the correct answer from the options given below : [2025]

Q 37 :
In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $[M^{a} L^{b} T^{c}]$ . If b = –3, the value of c is __________. [2025]