Fundamental and Derived Unit and Quantities

Q 1 :

The density of a material in SI units 128 kg $m^{- 3}$ . In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is [2019]

410
640
16
40

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(4)

Density $ρ = \frac{M}{L^{3}}$

$n_{1} u_{1} = n_{2} u_{2}$

$∴ 128 [M_{1} L_{1}^{- 3}] = n_{2} [M_{2} L_{2}^{- 3}]$

$∴ n_{2} = 128 [\frac{M_{1}}{M_{2}}] {[\frac{L_{2}}{L_{1}}]}^{3} = 128 \times [\frac{1000}{50}] \times {[\frac{25}{100}]}^{3}$

$= 128 \times 20 \times \frac{1}{64} = 40$

Q 2 :

If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E/H will be [2021]

joule
ohm
newton
mho

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4

(2)

Unit of $\frac{E}{H}$ is $\frac{v o l t / m e t r e}{A m p e r e / m e t e r} = \frac{v o l t}{A m p e r e} = o h m$

Q 3 :

Match List l with List II. [2021]

List I List II

a) $R_{H}$ (Rydberg constant) (i) $k g m^{- 1} s^{- 1}$

b) $h$ (Planck's constant) (ii) $k g m^{2} s^{- 1}$

c) $μ_{B}$ (Magnetic field energy density) (iii) $m^{- 1}$

d) $η$ (Coefficient of viscosity) (iv) $k g m^{- 1} s^{- 2}$

Choose the most appropriate answer from the options given below:

(a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)
(a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)
(a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)
(a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)

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(1)

SI unit of Rydberg constant = $m^{- 1}$

SI unit of Plank's constant = $k g m^{2} s^{- 1}$

SI unit of Magnetic field energy density = $k g m^{- 1} s^{- 2}$

SI unit of Coefficient of viscosity = $k g m^{- 1} s^{- 1}$

Q 4 :

Match List I with List II. [2022]

List I List II

A. Torque I. $N m s^{- 1}$

B. Stress II. $J K g^{- 1}$

C. Latent Heat III. $N m$

D. Power IV. $N m^{- 2}$

Choose the correct answer from the options given below:

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

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(2)

Torque = $F \times r_{⊥} N m$

Stress = $\frac{F o r c e}{A r e a} = N / m^{2}$

Latent heat = $\frac{E n e r g y}{M a s s} = J K g^{- 1}$

Power = $\frac{W o r k}{T i m e} = N m s^{- 1}$

Q 5 :

Given below are two statements: [2023]

Statements I: Astronomical unit (Au). Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.

Statements II: Au < Parsec (Pc) < ly

In the light of the above statements. choose the most appropriate answer from the options given below:

Both Statements I and Statements Il are correct.
Statements I is correct but Statements II is incorrect.
Both Statements I and Statements II are incorrect.
Statements I is incorrect but statements II is correct,

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(2)

$1 AU = 1.496 \times 10^{11} m$

$1 par sec = 3.08 \times 10^{16} m$

$1 light year = 9.46 \times 10^{15} m$

$S o, A u < l y < P a r s e c$

Q 6 :

Consider a block and trolley system as shown in the figure.
If the coefficient of kinetic friction between the trolley and the surface is 0.04, the acceleration of the system in $m^{- 2}$ is:
(Consider that the string is massless and un-stretchable and the pulley is also massless and frictionless). [DEMO]

3
4
2
1.2

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DEMO

Q 7 :

Match List I with List II

List I List II

(A) Magnetic induction (I) $Ampere {meter}^{2}$

(B) Magnetic intensity (II) Weber

(C) Magnetic flux (III) Gauss

(D) Magnetic moment (IV) Ampere/meter

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

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

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(2)

(A) Magnetic induction	Gauss (III)
(B) Magnetic intensity $(H = \frac{B}{μ})$	Ampere/meter (IV)
(C) Magnetic flux $\to ϕ = \vec{B} \cdot \vec{A}$	Weber (II)
(D) Magnetic moment $\vec{M} = I \vec{A}$	$Ampere - {meter}^{2}$ (I)

Q 8 :

Match List-I with List-II

List I List II

(A) Heat capacity of body (I) ${Jkg}^{- 1}$

(B) Specific heat capacity of body (II) ${JK}^{- 1}$

(C) Latent heat (III) ${Jkg}^{- 1} K^{- 1}$

(D) Thermal conductivity (IV) ${Jm}^{- 1} K^{- 1} s^{- 1}$

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

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

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(4)

Heat capacity = J/K, A $\to$ II

Specific heat capacity III = J/kgK, B $\to$ III

Latent heat = J/kg, C $\to$ I

Thermal conductivity, k $\equiv \frac{Q}{A} \frac{△ x}{△ T} \equiv$ J/mKs, D $\to$ IV

Q 9 :

Given below are two statements:

Statements I: Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.

Statements II: Au < Parsec (Pc) < ly

In the light of the above statements. Choose the most appropriate answer from the options given below: [2023]

Both Statements I and Statements II are correct.
Statements I is correct but Statements II are incorrect.
Both Statements I and Statements II are incorrect.
Statements I is incorrect but Statements II is correct.

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(2)

1 AU = $1.496 \times 10^{11} m$

1 par sec = $3.08 \times 10^{16} m$

1 lyght year = $9.46 \times 10^{15} m$

So, Au < ly < Par sec.

Q 10 :

Which one of the following is not a measurable quantity? [2026]

Resistance
Voltage difference
Displacement current
Voltage

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(4)

Here from voltage, question refers to potential. We can measure potential difference between two points but not potential at any point.

Note: If the potential of reference point is known then we can measure potential as well.

Q 11 :

If $ε_{0}, E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $\frac{ε_{0} E}{t}$ will be : [2026]

$Am$
${Am}^{2}$
$A / m^{2}$
$A / m$

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(3)

$E = \frac{Q}{A ε_{0}} \Rightarrow [ε_{0} E] = \frac{A T}{L^{2}}$

$[\frac{ε_{0} E}{t}] = \frac{A}{L^{2}} \Rightarrow Unit is (A / m^{2})$

Q 12 :

A new unit $(α)$ of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $α$ units if light takes 6 min 40 s to cover this distance? [2026]

200 $α$
400 $α$
300 $α$
500 $α$

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(2)

$α = 3 \times 10^{8} m$

$6 min 40 sec = 6 \times 60 + 40 = 400 sec$

${Distance=(400)×3×10}^{8} m = 400 α$

Topic Question Set

Q 1 :

The density of a material in SI units 128 kg $m^{- 3}$ . In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is [2019]

Q 2 :

If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E/H will be [2021]

Q 4 :

Match List I with List II. [2022]

List I List II

A. Torque I. $N m s^{- 1}$

B. Stress II. $J K g^{- 1}$

C. Latent Heat III. $N m$

D. Power IV. $N m^{- 2}$

Choose the correct answer from the options given below:

Q 7 :

Match List I with List II

List I List II

(A) Magnetic induction (I) $Ampere {meter}^{2}$

(B) Magnetic intensity (II) Weber

(C) Magnetic flux (III) Gauss

(D) Magnetic moment (IV) Ampere/meter

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

Q 10 :

Which one of the following is not a measurable quantity? [2026]

Q 11 :

If $ε_{0}, E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $\frac{ε_{0} E}{t}$ will be : [2026]

Q 12 :

A new unit $(α)$ of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $α$ units if light takes 6 min 40 s to cover this distance? [2026]

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	List I		List II
a)	$R_{H}$ (Rydberg constant)	(i)	$k g m^{- 1} s^{- 1}$
b)	$h$ (Planck's constant)	(ii)	$k g m^{2} s^{- 1}$
c)	$μ_{B}$ (Magnetic field energy density)	(iii)	$m^{- 1}$
d)	$η$ (Coefficient of viscosity)	(iv)	$k g m^{- 1} s^{- 2}$

	List I		List II
A.	Torque	I.	$N m s^{- 1}$
B.	Stress	II.	$J K g^{- 1}$
C.	Latent Heat	III.	$N m$
D.	Power	IV.	$N m^{- 2}$

	List I		List II
(A)	Magnetic induction	(I)	$Ampere {meter}^{2}$
(B)	Magnetic intensity	(II)	Weber
(C)	Magnetic flux	(III)	Gauss
(D)	Magnetic moment	(IV)	Ampere/meter

	List I		List II
(A)	Heat capacity of body	(I)	${Jkg}^{- 1}$
(B)	Specific heat capacity of body	(II)	${JK}^{- 1}$
(C)	Latent heat	(III)	${Jkg}^{- 1} K^{- 1}$
(D)	Thermal conductivity	(IV)	${Jm}^{- 1} K^{- 1} s^{- 1}$

Topic Question Set

Q 1 : The density of a material in SI units 128 kg m-3. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is [2019]

Q 2 : If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E/H will be [2021]

Q 3 : Match List l with List II. [2021] List I List II a) RH (Rydberg constant) (i) kg m-1 s-1 b) h (Planck's constant) (ii) kg m2 s-1 c) μB (Magnetic field energy density) (iii) m-1 d) η (Coefficient of viscosity) (iv) kg m-1 s-2 Choose the most appropriate answer from the options given below:

Q 4 : Match List I with List II. [2022] List I List II A. Torque I. Nms-1 B. Stress II. J Kg-1 C. Latent Heat III. Nm D. Power IV. Nm-2 Choose the correct answer from the options given below:

Q 7 : Match List I with List II List I List II (A) Magnetic induction (I) Ampere meter2 (B) Magnetic intensity (II) Weber (C) Magnetic flux (III) Gauss (D) Magnetic moment (IV) Ampere/meter Choose the correct answer from the options given below : [2025]

Q 8 : Match List-I with List-II List I List II (A) Heat capacity of body (I) Jkg–1 (B) Specific heat capacity of body (II) JK–1 (C) Latent heat (III) Jkg–1K–1 (D) Thermal conductivity (IV) Jm–1K–1s–1 Choose the correct answer from the options given below : [2025]

Q 10 : Which one of the following is not a measurable quantity? [2026]

Q 11 : If ε0, E and t represent the free space permittivity, electric field and time respectively, then the unit of ε0Et will be : [2026]

Q 12 : A new unit (α) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of α units if light takes 6 min 40 s to cover this distance? [2026]

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Q 1 :

The density of a material in SI units 128 kg $m^{- 3}$ . In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is [2019]

Q 2 :

If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E/H will be [2021]

Q 4 :

Match List I with List II. [2022]

List I List II

A. Torque I. $N m s^{- 1}$

B. Stress II. $J K g^{- 1}$

C. Latent Heat III. $N m$

D. Power IV. $N m^{- 2}$

Choose the correct answer from the options given below:

Q 7 :

Match List I with List II

List I List II

(A) Magnetic induction (I) $Ampere {meter}^{2}$

(B) Magnetic intensity (II) Weber

(C) Magnetic flux (III) Gauss

(D) Magnetic moment (IV) Ampere/meter

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

Q 10 :

Which one of the following is not a measurable quantity? [2026]

Q 11 :

If $ε_{0}, E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $\frac{ε_{0} E}{t}$ will be : [2026]

Q 12 :

A new unit $(α)$ of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $α$ units if light takes 6 min 40 s to cover this distance? [2026]