Summary of si units - class-VIII

The kilogram represents the unit of a physical quantity and not the physical quantity

Unit of mass is kilogram and here, kilo is a prefix used in the unit. Thus mass is the physical quantity which has prefix with its unit.

$I = AT^2 e^{-B/kT}$
Dimensionally, $A = I/T^2$, dimensions of B = kT
($\because$ power of exponential is a number)
$\displaystyle AB^2 = \frac{I}{T^2} (kT)^2 = Ik^2$

Relative density is a unitless quantity. Thus the given statement is false.

Given F = A / (B + sqrt(d)), for the equation to be dimensionally consistent, B must have the same dimensions as sqrt(d), which is (ML^-3)^0.5 = M^0.5 L^-1.5. Since F = [MLT^-2], then A = F * (B + sqrt(d)) = [MLT^-2] * [M^0.5 L^-1.5] = M^1.5 L^-0.5 T^-2.

Illuminance is luminous flux per unit area, it is measure in 'lux'.

Change in momentum $=Force \times time=dyne-sec$

'Second' is a fundamental unit.

Atmospheric pressure is measured in bar.

Candela is the unit of Luminous intensity.
Watt is the unit of power.
Lumen is the unit of luminous flux.
Ampere is the unit of current.

Siemen is the unit of Electrical conductance.
Siemens/meter is the unit of Electrical conductivity.
Voltage is the unit of Potential difference.
Henry is the unit of Inductance.

A: eg. $10$ seconds, where $n=10, u=$seconds. This is constant.
B: We can choose any quantity as fundamental and derive other quantities with respect to that

Parsec, light year and micron are all units of length. 

The correct option is D.

The Debye, represented as D, is a CGS unit of electric dipole moment. This name was given in the honor of the physicist Peter J. W. Debye. Its value is defined as $1 \times { 10 } ^{ -18 }$ statcoulomb-centimetre.

The SI unit of luminous intensity is Candela

Mole represents the amount of substance in the SI system of units.

SI unit of temperature is Kelvin denoted by  $K$.

Milligram is a submultiple of Kilogram.

Frequency of a wave is measured in hertz  $(Hz)$.

Parallactic second is a unit of distance.

Absolute permittivity $(\epsilon)$ is the measure of the resistance that  is encountered when forming an electric field in a medium. The standard SI unit for absolute permittivity is Farad per meter $(F/m)$.

Dimensonal constants are those constants while have both fixed magnitude and dimension.

SI unit of electric energy or heat energy is Joule (J). One Joule is defined as the amount of energy exerted when a force of one newton is applied over a displacement of one meter. One Joule is equivalent of one watt of power radiated or dissipated for one second.

The strength of a force is expressed by its magnitude. The magnitude of a force is expressed in the SI unit of force called Newton. One Newton is the force which can make an object of one kilogram mass to move at a speed of one meter per second.

Mole is standard unit to measure the amount of substance in SI system.
The mole is the amount of substance which contains as many elementary entities  present in atoms in 0.012 kg of carbon-12.

Temperature is a fundamental quantity, so it can not be expressed as a derived quantity in terms of length, mass and time.So the correct option is (D).

In the equation x = a + bt + ct^2, all terms must have the same units as x. Since x is in meters, the constant 'a' must also have units of meters.

Joule is a unit for work done and coulomb is the unit for the charge. The potential is defined as the ratio of the work done to the charge and the unit of the potential difference is volt. Hence, one joule per coulomb is equal to the unit of the potential difference. Therefore it will be equal to one Volt.

$\sqrt{\dfrac{\varepsilon _0}{\mu _0}}=\sqrt{\dfrac{\varepsilon _0^2}{\mu _0\varepsilon _0 }}=\varepsilon _0c=[M^{-1}L^{-3}T^{4}A^2][LT^{-1}]$
$[M^{-1}L^{-2}T^{3}A^2]$

Latent heat is related to the heat energy as:
$Q=mL$
$\displaystyle L=\frac {Q}{m}=Jkg^{-1}$

Fundamental unit $\rightarrow$ $Kg$
Derived unit $\rightarrow$ $N$
Practical unit $\rightarrow$ $Kg-Wt$
Supplementary unit $\rightarrow$ $rad$