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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(D) 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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(B) 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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(A) 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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(B) 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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(B) $1 A U = 1.496 \times 10^{11} m$

$1 p a r s e c = 3.08 \times 10^{16} m$

$1 l i g h t y e a r = 9.46 \times 10^{15} m$

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

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

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:

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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.	$N m^{- 2}$

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:

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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: