Units - definitions and systems - class-XII

Metre is the SI unit of length.

Second is a standard unit of time. Thus the given statement is false.

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

Knot is a measure of the speed of ship. The term knot dates from the 17th century, when sailors measured the speed of their ship by using a device called a "common log".

 A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. There are seven basic fundamental quantities: Length, mass, time, electric current, amount of substance, luminous intensity and temperature. So, the base quantity among the following is length.

$l=20\pm 0.01, B=10\pm 0.02$

The Gauss (G), is the cgs unit of measurement of magnetic flux density (B). One gauss is defined as one maxwell per square centimeter.

The debye (symbol: D) is a CGS unit of electric dipole moment, named in the honour of the physicist Peter J. W. Debye.
It is defined as $ 1\times { 10 }^{ -18 }$ statcoulomb-centimetre.

The SI unit for mass is the kilogram (kg). Grams and milligrams are sub-units, while milliliters are a unit of volume.

 The CGS unit of energy is erg. The erg is a unit of energy equal to $10^{-7}$ joules.

Watt is unit of power, hour is unit of time. 

In C.G.S system, Maxwell is the unit of magnetic flux 
$1 Wb(S.I unit)=10^8\ maxwell$

(3) Ampere
Because Calorie,Joule and Kelvin are related to Heat.
But, Ampere is the unit of current.

Electromotive force is the voltage developed by any source of electrical energy such as a battery or dynamo. It is generally defined as the electrical potential for a source in a circuit.

Susceptibility is unit less.
Magnetic flux is expressed $Vs$ or $[M^1L^2T^{-2}A^{-1}] = JA^{-1}$.

The metric system in weights and measures was adopted by the Indian Parliament in December 1956 with the Standards of Weights and Measures Act, which took effect beginning 1 October 1958. 

Henry is the unit of Inductance.
Volt is the unit of emf.
Farad is the unit of capacity.
$(\dfrac{1}{\rho})$ is the unit of conductivity.

The International System of Units, universally abbreviated S.I. is the modern metric system of measurement. The S.I. was established in 1960 by the 11th General Conference on Weights and Measures.

Impulse is defined as the change in momentum and thus impulse has the unit of momentum i.e.  $kg \ m/s$

The velocity gradient is defined as the change in velocity per unit distance.

Light travels at approximately 300,000 kilometers per second in a vacuum, which has a refractive index of 1.0, but it slows down to 225,000 kilometers per second in water (refractive index = 1.3) and 200,000 kilometers per second in glass (refractive index of 1.5). The interaction of the light with the particles in the medius causes the delay.

Gram and kilogram are the units of mass whereas newton is the unit of weight (force).

S.I system (standard international system). 

One of the properties of the units is standard unit should be reproducible. It means that the standard unit can be used repetitively to retain consistency of units, independent of space and time.

SI unit of magnetic field is  $Weber/m^2$. Other units of magnetic field are $Tesla$ and $Gauss$.
Also,  $1 \ Tesla = 10^4 \ Gauss$

Candela is the SI unit of intensity of light.

1.  For Speed :

Diameter of human hair is $50000$nm.

$kgm^2s^{-2}$ is the unit of energy. It's dimension is $[ML^2T^{-2}]$ All the quantities given in the option are different form of energy. So their units will be same. Then the unit $kgm^2s^{-2}$ is associated with all of the options.

Power is defined as the work done per unit time. So to get the SI unit of power :

$Power=\dfrac{Work}{Time}$

SI unit of Work $=$ Joules

SI unit of Time $=$ second

So S.I. unit of power $=\dfrac{Joule}{Second}=Watt$

Rad is the unit of absorbed dose of ionizing radiation. One rad is equal approximately to the absorbed dose delivered when soft tissue is exposed to one-roentgen of medium-voltage radiation. Thus this is the bilogical effect of radiation.

1. They symbol named after scientist should have the capital letter, 

The gram per cubic centimetre is a unit of density in the CGS system, defined as mass in grams divided by volume in cubic centimetres.

Heat is a form of energy that flow from a hotter body to a colder one.

Calorie is defined as the amount of heat energy needed to raise the temperature of one gram of pure water by one degree Celsius. $1$ Kilocalorie are $1000$ calories, the amount of caloric energy needed to raise the mass of$1$ kg of pure water by $1^0C$. $1$ kilocalorie is $4200$ Joules.

Standard unit does not change with respect to time and space. Thus option B is correct.

The S.I. unit of temperature as per the International System of Units is Kelvin which is represented by the symbol $K$. The Kelvin scale is widely accepted or used in the field of science and engineering.

The main quantity that measures the motion of a body is momentum. An object's momentum increases with the object's mass and with its velocity.

When current $ I $ flow in the circular loop of area $a$ than , magnetic moment will be $M=Ia= Am^2$

Ampere-hour is the unit of quantity of electricity or quantity of electric charge.

The universal gravitational constant G has a standard value of approximately 6.673 * 10^-11 Nm^2/kg^2.

Strain is defined as the ratio of change in dimension to the original dimension. Since it is a ratio of two identical physical quantities, it is a dimensionless quantity.

Permeability (mu) is related to magnetic field intensity H and magnetic flux density B by B = muH. The SI unit of B is Tesla (T) and H is Ampere per metre (A/m), so mu = B/H has units of T/(A/m) = Tm/A. Henry per metre (H/m) is also a standard unit, and Weber per ampere metre (Wb/A*m) is equivalent to H/m.

The given relation is ${ Iq }{ Z } $, since $q=It$.

The ratio of electric field intensity E (V/m) to magnetic field intensity H (A/m) is known as the intrinsic impedance of the medium. The unit is (V/m) / (A/m) = V/A, which is the definition of an Ohm.

Joule and Calorie are units of energy. Kelvin is the SI unit of thermodynamic temperature, not energy.

Surface tension is force per unit length (N/m). Since N = kg*m/s^2, N/m = kg/s^2. Also, surface tension is energy per unit area (J/m^2). Watt/meter is power per unit length, which is not surface tension.

In the equation (P + a/V^2)(V - b) = RT, the term a/V^2 must have the same units as pressure P. Thus, units of a = units of P * units of V^2. Pressure is force/area (dyne/cm^2 in CGS) and volume is length^3 (cm^3). So, a = (dyne/cm^2) * (cm^3)^2 = dyne * cm^4.

Acceleration has unit $m/{s}^{2}$.

SI unit system contains seven fundamental quantities which are independent to each other and can be used to represent any given quantity. Hence, all physical quantities can be represented in powers of seven fundamental SI units.

Gradient of a quantity $Q$ is given as $\dfrac{\Delta Q}{\Delta x}$
Thus, a gradient will be unitless if its numerator has same dimensions as denominator, i.e. $x$ (which has the dimension $L$).
Thus, out of the options, Displacement has the dimension $L$ and hence its gradient will be dimensionless.

The unity of density$=\frac { unit\quad of\quad mass }{ { (unit\quad of\quad length) }^{ 3 } } \ =(pails){ (Jack) }^{ 3 }$

The weight of a body is , as the force with which the earth attracts it towards the centre.

$W= \dfrac{GMm}{R^2 }= mg$

$g$ (acceleration due to gravity) $= \dfrac{GM}{R^2}$

where,

$G$ is constant of gravitation, $R$ is distance from the centre if the earth, $M$ is the mass of the earth.

If the mass of the body $‘m'$ , the force of attraction of the earth or the $‘W'$ of the body is

$W= mg$

Weight is the force of attraction, its S.I. unit is same as that of S.I. unit of force .

The S.I. unit of weight is Newton (N).

The magnitude of a physical quantity represent the amount contained in the quantity. Therefore, the magnitude of the quantity consists of a number only.

We know that, 

Percentage determines the accuracy in the measurement. More is the percentage of error, more is the error in the measurement.

We know that $1 \ mm = 0.039 \ inch$ 

Since the numbers $0.310$ and $103$ have 3 significant figures each. In the case of the multiplication, the maximum number of significant figures is the same as that of the number of significant figures in decimal number., so the final answer must also have 3 significant figures.

The steradian (symbol: sr) or square radian is the S.I. unit of solid angle. It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planer angles.

Pressure is measured in Pascal $(Pa)$.

Angular velocity and angular frequency have the same dimension  $[T^{-1}]$.

Among the given units kilogram is the fundamental or base unit whereas others are the derived units.

Mass is property of mater, which is independent of other properties like temperature, pressure or location of the object in space.

The gradient of any physical quantity is computed to as per unit length. This means it is a rate with respect to length. So, the Displacement gradient will also be length per unit length. Because a displacement gradient is the ratio of two quantities having dimensions of "length". That is, a displacement gradient has units of a meter per meter for example. 

The length dimensions will be cancelled, and we have a unitless quantity. While others will be having certain units. Hence it is a unitless quantity.

Thus option B is correct.

An atmosphere is defined as the unit of pressure because we use to write the atmospheric pressure in terms of the $atm$.