Fundamental quantities - class-VII

The specific latent heat of a substance is the quantity of heat energy required to change the state of a unit mass of a substance.

The specific heat capacity  of a substance is the heat needed to raise

the temperature of 1 kg of the substance by 1K (or by ${1}^{0}C$).
The specific heat capacity of water is $4200 J{kg}^{-1}{K}^{-1}$.

The heat or thermal capacity of a defined system is the amount of heat required to raise the system's temperature by one degree. It is expressed in units of thermal energy per degree temperature.

Potential is work done per unit charge $\displaystyle =\frac {J}{c}$

Watt is  the SI unit of power, equivalent to one joule per second.

The pascal (symbol: Pa) is the SI derived unit of pressure, internal pressure, stress, Young's modulus.

Capacitance is charge per unit volt. 

The correct option is D.

The magnetic permeability of any material is its property for allowing the magnetic line of force to pass through it. Therefore, the magnetic material can support the development of the magnetic field. This capability is measured by the magnetic permeability. Also, the magnetic line of force is directly proportional to the conductivity of the material. Its SI unit is Henry per meter i.e. $Hm^{-1}$ or newton per ampere square.

Electric energy $=ML^{2}T^{-2}$
Electric power $=ML^{2}T^{-3}$
Electric resistance $= ML^{2}I^{-2}T^{-3}$
Electric capacity $=M^{-1}L^{-2}I^{2}T^{4}$$=\left ( \dfrac{I^{2}T^{2}}{(M^{1}L^{2}T^{-2})} \right )=\left ( \dfrac{Q^{2}}{J} \right )$
Hence, option C is correct.

Joule is unit of heat , energy and work.

There are seven fundamental units in the SI system of units which are mass, length, time, temperature, electric current, mole and luminous intensity.

Mass of a body is defined as the quantity of matter contained in a body.

The units which can neither derived from one another nor resolved into any thing more basic are called fundamental unit. It is independent of any other unit.

One second is defined to be equal to $9,19,26,31,770$ periods of cesium clock.

The dimesnion of $k $ is $M^1T^1L^{-3}\theta^{-1}$

Dimensional formula of the following are given as-

Dimensional formula of the following are given as-

We know that the fundamental quantities are mass, length and time. 

In dimensional analysis, only commensurable quantities may be compared, equated and added or subtracted.

Light year is a unit of $distance$.

Time is generally represented by the symbol $t$.
Mass is represented by symbol $m$ and force by the symbol $F$.

Electric field due to a charge is given by  $E = \dfrac{F}{q}$
Unit of force is Newton $(N)$ and that of charge is Coulomb $(C)$.
So, unit of electric field is  Newton/coulomb  i.e  $N/C$

The derived quantities are gravitational constant, frequency, electric charge because they are made up of several other quantities combined to form one single quantity.

The energy which an electron acquires when accelerated, through a potential difference of 11 volt is called 1 eV. It is a unit of energy.  It is usually used as a measure of particle energies although it is not an SI (System International) unit. The SI unit for energy is the Joule. $1,eV=1.602\times 10^{-19},Joules$

SI unit of Length $=$ meters.

New Unit of Length $=x$ meters.

$1m=\dfrac 1x$ new units

SI unit of area : 

$A= 1m^2$   

$=1\times 1m^2$                        

$=\dfrac 1x\times \dfrac 1x $     

$=\dfrac{1}{x^2}$     

Energy E = M L^2 T^-2 = 10^7 erg = 1 Joule. Force F = M L T^-2 = 10^5 dyne = 1 Newton. Time T = 1 second. Using F = M L T^-2 and E = F L, we get 1 Joule = 1 Newton * L, so L = 1 meter.

Unit of $\pi $ is radians.

Self inductance L has the SI unit Henry (H), which equals volt-second/ampere. From V = L(dI/dt), dimensionally [H] = [V][T]/[A]. Option B: joule×second/(coulomb×ampere) = (V×C×T)/(C×A) = V×T/A = Henry, which is correct. Note that 'coubmb' in option B appears to be a typo for coulomb.

The term epsilon_0 * (d_phi / dt) is the displacement current in Maxwell's equations, which has the same dimensions as electric current.

Electric capacitance of a conductor is the ability with which the conductor can hold the charge.
In SI system, unit of capacitance is farad($F$).
Hence, option D is not matched.

$\text{Kilowatt hour}$ is the $commercial$ unit of $electrical$ ENERGY.

The intensity of magnetic field at a point on the field is defined as the force on a unit north pole placed at that point.
Intensity of magnetization is measured in Oersted as a unit.

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. It is defines as force per unit area. The SI unit of pressure is $N/m^2$.

Damping force F = -bv, where v is velocity. Thus, b = F/v. Units of b = (kg * m / s^2) / (m / s) = kg / s.

In the equation S = a + bt + ct^2, each term must have the same units as S (meters). Thus, ct^2 must be in meters. c * (s^2) = m, so c = m / s^2 = m * s^-2.

Let us take side of cube$=a$
then  $a^3=6a^2$
$\therefore a=6$
So volume of cube is:

Units of both $P $ and $ \dfrac {a}{V^2}$ must be same.
So, $\dfrac {a}{V^2}=P$  $\implies   a=PV^2$ 

Specific resistance of a material is given by

Speed, density and force are the derived physical quantities whereas time is the fundamental physical quantity.

There are only $7$ fundamental physical quantity out of which mass is a fundamental quantity.

Displacement, force, and velocity are vector quantities as they require direction as well as the magnitude for their representation but the kinetic energy is a scalar quantity as it does not require direction for its representation.

Dimensional analysis establishes the relation between the physical quantities by comparing the different quantities using their fundamental dimensions.

F = ma = kgms-2

SI unit of force is Newton(W)

Hence, newton is a derived unit

A dimensionless quantity is that is always independent of basic $7$ units:-meter, second, kilogram, Kelvin, Candela, ampere.

i. GM_eM_s is energy related (potential), ii. 3RT/M is velocity squared (m^2/s^2), iii. F^2/q^2B^2 is velocity squared, iv. GM_e/R_e is velocity squared. Matching these to the provided units leads to B.

Conductivity (or specific conductance) of an electrolyte solution is a measure of its ability to conduct electricity. The SI unit of conductivity is siemens per meter $(S/m)$