Fundamental and derived quantities - class-XI

Among the given units watt is the unit of power whereas all others are the units of energy.

Calorie, kilowatt hour, joule all are the units of energy whereas watt is the unit of power.

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 $=\dfrac{Joule}{Second}=Watt$

$1000\,Watt=1\,Kilowatt$

The magnitudes of physical quantities can be added together or subtracted from one another only if they have the same dimensions. 

Force, power times time (energy), and rate of change of momentum (force) all have units of Newtons or Joules. Distance/energy has units of m/J, which is different from the others.

The pascal $(Pa)$ is the SI derived unit of pressure used to quantify internal pressure, stress, Young's modulus and ultimate tensile strength. The unit, named after Blaise Pascal, is defined as one newton per square metre.

The second derivative of energy (J) with respect to distance (m) is d^2(J)/d(m)^2, which results in J/m^2.

We measure the intensity of radioactive emission by  number of atoms that get transformed to new atoms per unit time. 
Curie(Ci) is the standard unit used for measuring radio-activity.
Curie is defined as the emission rate of 1g of radium which is equal to $3.7 \times 10^{10}$ transformations per second.

Electrons spinning on their axes are magnetic dipoles that may or may not cancel out each other depending on the type of dipole.
We measure the  magnetic moment of electron in Joule / Tesla.
The value of magnetic dipole of an electron is $9.27 \times 10^{-24}$ Joule/Tesla.   

The kilowatt-hour ( kWh) is a unit of energy equal to 3600 kilojoules. The kilowatt-hour is a composite unit of energy equal to one kilowatt (kW) of power sustained for one hour.

Gravitational Potential Energy, $U=mgh$

Mass, Length & Time are fundamental physical quantity while velocity is derived physical quantity.

Temperature is one of the basic (fundamental) physical quantities.

CGS. units of density. is $g cm^{-3}$ where as in MKS unit it is $kg/m^3$.

We get Kilogram metre per second as the MKS units of force.

$1$ $hp = 745.699872 W$. 

Work done by a force   $W = FS$
Units of work   $W = kg.ms^{-2}\times m = kg \ m^2 \ s^{-2}$

The newton (symbol: N) is the International System of Units (SI) derived unit of force which is equivalent to $kg  m  { s }^{ -2 }$

1 joule (or 1J) is expressed in other SI units as $kg  { m  }^{ 2 } { s }^{ -2 }$

$1$ newton (or $1\ N$) is expressed in other SI units as $kg  m  { s }^{ -2 }$.

1 pascal (or 1Pa) is expressed in other SI units as $kg  { m }^{ -1 }  { s }^{ -2 }$

$Js$ $\rightarrow  M^{1} L^{2} T^{-1}$
Energy $= M^{1} L^{2} T^{-2}$
Angular Momentum $= mvr = M^{1} L^{2} T^{-1}$
Momentum $= mv = M^{1} L^{1} T^{-1}$
Power $= f\times v = M^{1} L^{2} T^{-3}$
Hence, option B is correct.

Joule is not the unit of force, it is the SI unit of work.

Mass, length and time are the fundamental physical quantities whereas density is the derived physical quantity.

The effect of an impulse force on the body is measured only in terms of impulse. If a moving object is stopped by an impact, the change in momentum of the object occurs. This change in momentum is called the impulse.

$W \ s$, $kWh$ and $erg$ are the unit of energy but $J \ s$ is not the unit of energy. So, energy cannot be measured in $J \ s$

Momentum $=$ mass X velocity  $=kg\dfrac { meter }{ { sec } } $

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. Any unit which can be obtained by the combination of one or more fundamental units is called derived unit.

Relative density is the ratio of density of a substance to the density of a given reference material. Thus, it is a unit less quantity. Hence, the given statement is false.  

An atmosphere is a unit of pressure.

The fundamental quantities are basically mass, length,  time etc. Velocity is defined as the rate of displacement with respect to time. Displacement has dimensions same as that of length. Velocity is a derived quantity. Acceleration is defined as the rate of change of velocity with respect to time. This is how when acceleration is dependent on time and velocity. It is also a derived quantity. Density is defined as the mass of a unit volume of a substance. Volume has the dimension of the cube of length. Hence density is also a derived quantity.

Unit of angle is radian, that of luminous intensity is candela and that of current is Ampere. Coefficient of friction is unitless and dimensionless.

Using the equation: $ Energy = Power\  delivered \times  Time $
We can see that unit of energy or work done can also be written as product of units of power and time.

The value of g = 9.80665 $m/s^{2}$. This means that for every second that elapses, velocity changes 9.80665 meters per second.

Stefan's law states P = sigma * A * T^4. Rearranging for sigma gives P/(A * T^4), which has units of Watt/(m^2 * K^4).

The SI unit of a modulus is the pascal $(Pa)$. A higher modulus typically indicates that the material is harder to deform.

The magnetic field B is related to force by F = I * L * B. Thus, B = F/(I * L) = Newton/(Ampere * meter). Since 1 Tesla = 1 Weber/m^2, the units of permeability (mu = B/H) involve Weber/(Ampere * meter).

Faraday is the charge of 1 mole of electron
That is, $6.022 \times { 10 }^{ 23 } \times 1.60217646 \times { 10 }^{ -19 }\ = 9.65 \times { 10 }^{ 4 } C/g-equivalent \ = 9.65 \times { 10 }^{ 7 }C/kg-equivalent$

Heat capacity is a physical property of matter, defined as the amount of heat to be supplied to a given mass of a material to produce a unit change in its temperature. The SI unit for heat capacity of an object is joule per kelvin ($J/K$ or $J k^{-1}$).

Power is defined as the rate of doing work, measured in Joules per second, which is defined as the Watt.

Angular momentum has units of (mass * velocity * radius), which is (kg * m/s * m) = kg * m^2/s. Since Joule = kg * m^2/s^2, Joule * second = (kg * m^2/s^2) * s = kg * m^2/s, matching angular momentum.

The expression B^2 / (2 * mu_0) represents the energy density of a magnetic field, which has the same units as pressure (energy per unit volume).

Answer is D.

The right matches are given below.

1. Mass                                   -  b. kilogramII. same everywhere
2. Weight                                -  d. Newton IV. depends on the altitude
3. Gravitational acceleration  -  a. $m/s^2$I. zero at the center
4. Gravitational constant        -  c. $Nm^2,,kg^{-2}$III. remain constant in the universe

Mass is intrinsic nature of any object or material and it doesn't vary or depend on gravitational field around it.
Weight is the force experienced by an object and it depends on both the mass as well as gravitational field which it experiences in a particular place.

Every unit of length has a corresponding unit of area, namely the area of a square with the given side length. Thus areas can be measured in square kilometres, or ${ km }^ { 2 }$.

SI unit of mass is Kg , acceleration is $ms^{-2}$ ad of velocity is $ms^{-1}$.

Moment of inertia $=\dfrac { 1 }{ 2 } \times mass\times { \left( Radius\quad of\quad gyration \right)  }^{ 2 }= \left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ 0 } \right] $

CGS unit of force is dyne.

SI unit of potential energy is Joule $(J)$.

The spring balance is the device used for measurement of weight. The weight of a body is measured in terms of the newton. On the other hand, kilogram is the unit for the mass of the body.

Newton is the unit of force.

The derived quantities are the one which depends on the other fundamental quantities for their representation. Among the following quantities, an electric current is a fundamental quantity whereas gravitational constant, frequency and electric charge are the derived quantities.

 SI base units of resistivity are written as $Kgm^3s^{-1}C^{-2}$.

Dimensional formula of newton second $=\left[ \dfrac { kgm }{ { S }^{ 2 } } \times S \right] $

Steradian is a unit of solid angle. Symbol of steradian is Sr

(A) Speed $\displaystyle = \frac{distance}{time}$ - a derived quantity of length and time.
(B) Temperature - fundamental quantity.
(C) Volume (cube of length) - a derived quantity of length.
(D) Mass - fundamental quantity.