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Some examples of derived units - class-XI

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Which of the following units is a unit of power?

  1. Kilowatt hour

  2. Watt

  3. Erg

  4. Calorie


Correct Option: B
Explanation:

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

Spot out the odd one.

  1. calorie

  2. kilowatt hour

  3. joule

  4. watt


Correct Option: D
Explanation:

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

The unit of power is:

  1. $Kilowatt$

  2. $kWhv$

  3. $dyne$

  4. $joule$


Correct Option: A
Explanation:

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 velocity of a particle is given as $v = a + b t + c t ^ { 2 }$ .the velocity is measured in $\mathrm { ms } ^ { - 1 }$ , then units of a and c are

  1. $m s ^ { - 1 } \text { and } m s ^ { - 3 }$

  2. $m s ^ { - 2 } \text { and } m s$

  3. $m ^ { 2 } s \text { and } m s ^ { 2 }$

  4. $m s \text { and } m s ^ { - 1 }$


Correct Option: A
Explanation:

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

$[a]=[u]=ms^{-1}$

$[ct^2]=[v]=ms^{-1}$

$[c]=[\dfrac{v}{s^2}]=ms^{-1-2}$

$[c]=ms^{-3}$
Option A

Three of these quantities have the same unit. Which quantity has a different unit ?

  1. $\dfrac{distance}{energy}$

  2. $force$

  3. $power\times time$

  4. rate   of change of momentum


Correct Option: A

Pascal is a unit of 

  1. Pressure

  2. Force

  3. Linear momentum

  4. Energy


Correct Option: A
Explanation:

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 unit of $\dfrac{d^{2}y}{dx^{2}}$ is [where y is energy and x is distance]

  1. $\dfrac{J^{2}}{m^{2}}$

  2. $\dfrac{J^{2}}{m}$

  3. $\dfrac{J}{m}$

  4. $\dfrac{J}{m^{2}}$


Correct Option: D

Curie is the unit of 

  1. decay constant

  2. radio-activity

  3. half-life

  4. average life


Correct Option: B
Explanation:

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.

The magnetic moment of electron is :

  1. $ 9.27\times 10^{-24} $ Joule/Tesla

  2. $ 9.27\times 10^{-24} $ Tesla/Joule

  3. $ 9.27\times 10^{-23} $ Joule/Tesla

  4. $ 9.27\times 10^{-23} $ Tesla/Joule


Correct Option: A
Explanation:

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 is a unit of energy.

  1. True

  2. False


Correct Option: A
Explanation:

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

Unit of gravitational potential energy is ______.

  1. $J/s$

  2. $Js$

  3. $Nm$

  4. $N/m$


Correct Option: C
Explanation:

Gravitational Potential Energy, $U=mgh$


    $ =kg\times ms^{-2}\times m$


     $= Nm$    $ (kgms^{-2} =N)$

The $SI$ unit of specific heat capacity is $J\ kg^{-1}K^{-1}$.
What is the unit of specific heat capacity expressed in $SI$ base units?

  1. $ms^{-2}K^{-1}$

  2. $kgms^{-2}K^{-1}$

  3. $m^{2}s^{-2}K^{-1}$

  4. $kg m^{2}s^{-2}K^{-1}$


Correct Option: C
Explanation:
we know that J is the unit of work done 
So,
$J = kgm^2s^{-2} $
$\implies Jkg^{-1}K^{-1}= kgm^2s^{-2} \times kg^{-1}K^{-1}$
$\implies Jkg{-1}K^{-1}= m^2s^{-2}K^{-1}$
 
So, option C is correct answer.

Which of the following is a derived physical quantity?

  1. Mass

  2. Velocity

  3. Length

  4. Time


Correct Option: B
Explanation:

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

Temperature can be expressed as derived quantity in terms of the following

  1. Length and mass

  2. Mass and time

  3. Length, mass and time

  4. None of these


Correct Option: D
Explanation:

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

What is C.G.S unit of density?

  1. $g cm^{-3}$

  2. $g m^{-3}$

  3. $g cm^{-2}$

  4. $kg m^{-3}$


Correct Option: A
Explanation:

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

Newton is the unit of which quantity.

  1. Acceleration

  2. Force

  3. Mass

  4. Gravity


Correct Option: B
Explanation:

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

In the honor of famous scientist Sir Isaac Newton this unit is also called Newton. Hence newton is the SI unit of force.

One horse power is equal to

  1. $1000  W$

  2. $500  W$

  3. $764  W$

  4. $746  W$


Correct Option: D
Explanation:

$1$ $hp = 745.699872 W$. 

Approximately it will be $746  W$.

Which of the following is derived units of work?

  1. kg m$^2$ s$^{-2}$

  2. kg m$^2$ s$^{2}$

  3. kg m$^2$ s$^{-3}$

  4. kg m$^2$ s$^{-1}$


Correct Option: A
Explanation:

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

Write the derived S.I units of force.

  1. $Newton$

  2. $Pascal$

  3. $Mass$

  4. $Dyne$


Correct Option: A
Explanation:

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

How is the following derived unit related to the fundamental units?

1) joule

  1. $N m$$ s^{-1}$

  2. $Nm$

  3. $kg m$$^2 s^{-1}$

  4. $kg m$$^2 s^{-2}$


Correct Option: D
Explanation:

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

Newton is written in fundamental units as $kg\ m/s^{x}$. Value of $x$ is:

  1. 2

  2. 3

  3. 1

  4. -2


Correct Option: A
Explanation:

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

If pascal is written in fundamental units as kg m$^{-x} s^{-2}$,then $x$ is:

  1. $1$

  2. $2$

  3. $-1$

  4. $3$


Correct Option: A
Explanation:

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

Name the physical quantities related to joule.

  1. mass

  2. energy

  3. pressure

  4. intensity


Correct Option: B
Explanation:
Energy is measured in joule.

Write the derived unit of pressure.

  1. kg m$^{-1} s^{-2}$

  2. kg m$^{-2} s^{-2}$

  3. kg m$^{-1} s^{-1}$

  4. kg$^2$ m$^{-1} s^{-2}$


Correct Option: A
Explanation:
$Pressure=\dfrac{Force}{Area}=\dfrac{Mass \times Acceleration}{Area}$
$Pressure=kg\times ms^{-2}/m^2=kgm^{-1}s^{-2}$

Name the physical quantities which are measured in the $ns$.

  1. Time

  2. Mass

  3. Length

  4. Temperature


Correct Option: A
Explanation:
$1\ ns=10^{-9}\ seconds$
So the physical quantity measured in $ns$ is time.

$Js$ is the unit of

  1. Energy

  2. Angular Momentum

  3. Momentum

  4. Power


Correct Option: B
Explanation:

$Js$ $\rightarrow  M^{1} L^{2} T^{-1}$
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.

The SI unit of magnetic permeability is:

  1. ${ Am }^{ -1 }$

  2. ${ Am }^{ -2 }$

  3. ${ Hm }^{ -2 }$

  4. ${ Hm }^{ -1 }$


Correct Option: D
Explanation:
Magnetic permeability is a constant of proportionality that exists between magnetic induction and magnetic field intensity. 

In SI units, permeability is measured in henries per meter $H/m$ or $H m^{-1}$.

Which is not the unit of Force:

  1. Poundal

  2. Dyne

  3. Joule

  4. Newton


Correct Option: C
Explanation:

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

Which of the following is different from others ?

  1. Mass

  2. Length

  3. Time

  4. Density


Correct Option: D
Explanation:

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

Density is a ________ physical quantity.

  1. fundamental

  2. derived

  3. semi-derived

  4. semi-fundamental


Correct Option: B
Explanation:
Density is calculated from mass and volume by the relation   $\rho = \dfrac{m}{V}$
Since, density depends on other fundamental quantity for its measurement.
So, density is a derived physical quantity.

The effect of an impulse force on the body is measured only in terms of its

  1. Force

  2. Moment of momentum

  3. Impulse

  4. None of these


Correct Option: C
Explanation:

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.

Energy cannot be measured in

  1. $Js$

  2. $Ws$

  3. $kWh$

  4. $erg$


Correct Option: A
Explanation:

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

$ \dfrac{kg}{m^3} $ is an  S.I unit of density.

  1. True

  2. False


Correct Option: A
Explanation:

The density of a body is defined as the ratio of the mass to the volume of the body.

The SI unit of density is $\dfrac { Kg }{ { m }^{ 3 } } $.

SI unit of momentum is

  1. $dyne \cdot sec$

  2. $g\cdot cms^{-1}$

  3. $Ns$

  4. $gm\cdot s$


Correct Option: C
Explanation:

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

                    $ =$ force X time $=$ newton. second

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

  1. Fundamental unit

  2. Scale

  3. Derived unit

  4. Standard unit


Correct Option: C
Explanation:

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.

Unit of relative density is $kg\ m^{-3}$.

  1. True

  2. False


Correct Option: B
Explanation:

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.  

Derived units can be defined in terms of one or multiple fundamental units.

  1. True

  2. False


Correct Option: A
Explanation:
The units of fundamental quantities (length, mass,time) are known as fundamental units(meter, kilogram, second).
The derived quantities are the quantities defined in terms of fundamental quantities via a quantitative equation. Hence, the units of these fundamental quantities involved in the equation defines the derived units.
Hence, the given statement is true.

An atmosphere

  1. is a unit of pressure

  2. is a unit of force

  3. gives us an idea of composition of air

  4. is the height above which there is no air


Correct Option: A
Explanation:

An atmosphere is a unit of pressure.

$1$ Pa = $9.87\times 10^{-6}$  atm
Or   $1$ bar $ = 0.987$ atm

Which of the following has derived dimension?

  1. Velocity

  2. Acceleration

  3. Density

  4. All of the above 


Correct Option: D
Explanation:

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.

Which of the following physical quantities has neither dimensions nor unit?

  1. angle

  2. Luminous intensity

  3. Coefficient of friction

  4. Current


Correct Option: C
Explanation:

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

Coefficient of friction$=\dfrac{Applied force}{Normal reaction}$
$=\dfrac{[MLT^{-2}]}{[MLT^{-2}]}=$No dimensions
Unit $=\dfrac{N}{N}=$No unit.

Kilowatt hour (kWh) represents the unit of 

  1. Power

  2. Impulse

  3. Momemtum

  4. Energy


Correct Option: D
Explanation:

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.

SI unit of $g$ i.e. the acceleration due to gravity is 

  1. $m^2/s$

  2. $m/s^2$

  3. $s/m^2$

  4. $m/s$


Correct Option: B
Explanation:

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

Pressure depends on distance as, $P=\dfrac{\alpha}{\beta}exp\left(-\dfrac{\alpha z}{k\theta}\right)$, where $\alpha, \beta$ are constants, z is distance, k is Boltzmann's constant and $\theta$ is temperature. The dimension of $\beta$ are.

  1. $M^0L^0T^0$

  2. $M^{-1}L^{-1}T^{-1}$

  3. $M^0L^2T^0$

  4. $M^{-1}L^1T^2$


Correct Option: C
Explanation:
Given, 

$P=\dfrac{\alpha}{\beta}e^{\dfrac{-\alpha z}{k\theta}}$

Since, the exponentials are devoid of dimensions, the exponential part of the equation is ignored.  

Rest we have, $P=\dfrac{\alpha}{\beta}$

Since, $\dfrac{\alpha z}{k\theta}=Dimensionless$

$\alpha=\dfrac{k\theta}{z}$

Kinetic energy $=\dfrac 32 kT$

$k=\dfrac{K.E}{T}$

$\implies [k]=[M^1L^2T^{-2}][K^{-1}]$

$\implies [z]=[L^{-1}]$

$\implies [\theta]=[K^{-1}]$

From these, we get the values of $\alpha$ as,

$[\alpha]=[M^1L^1T^{-2}]$

Now, we know the dimension of prressure, 

$[P]=M^1l^{-1}t^{-2}]$

$\beta=\dfrac{\alpha}{P}$

$\implies \beta=\dfrac{[M^1L^1T^{-2}]}{[M^1L^{-1}T^{-2}]}$

$\implies \beta=[M^0L^2T^0]$

Which of the following is not the unit of mobility?

  1. $\frac { }{ V s } $

  2. $\frac { }{ ohm C } $

  3. ${ }{ V C } $

  4. $\frac {Cs }{ kg } $


Correct Option: C

The unit of Stefans constant $\sigma$ is:

  1. $\dfrac{{watt}^{4}}{m{K}^{4}}$

  2. $\dfrac{calorie}{{m}^{2}{K}^{4}}$

  3. $\dfrac{watt}{{m}^{2}{K}^{4}}$

  4. $\dfrac{joule}{{m}^{2}{K}^{4}}$


Correct Option: C

If $ \overline { A }  $ and $ \overline { B }  $ two different physical quantities, Which of the following mathematical operations is/are valid.

  1. $ \overline { A } $ + $ \overline { B } $

  2. $ \overline { A } .\overline { B } $

  3. $ \overline { A } \times \overline { B } $

  4. Both and (b) and (c)


Correct Option: D
Explanation:
Since $\vec A$ and $\vec B$ are different physical quantity, thus their unit will be different, only those quantity can be added or subtracted with each other if their units are same.
So, $\vec A+\vec B$  has no  and $\vec A\times \vec B$ physical significance were $\vec A.\vec B$ and $\vec A\times \vec B$are valid as they are the product operation 
Option $D$ is correct.


SI unit of modulus of elasticity is

  1. $pascal$

  2. $k g \cdot m / s ^ { 2 }$

  3. $N / m ^ { 2 }$

  4. $k g , m$


Correct Option: A
Explanation:

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

The SI unit of permeability of free space is

  1. $\cfrac { \text { weber } } { \text { ampere } }$

  2. $\cfrac { \text { henry } } { \text { ampere } }$

  3. $\cfrac { \text { tesla } } { \text { ampere-meter } }$

  4. $\cfrac { \text { weber } } { \text { ampere-meter } }$


Correct Option: D

The value of Faraday number in SI unit is:

  1. $ 9.65 coulomb/kg-equivalent $

  2. $ 9.65\times 10^7 coulomb/kg-equivalent $

  3. $ 9.65\times 10^{-7} coulomb/kg-equivalent $

  4. $ 9.65 \ coulomb/g  -equivalent $


Correct Option: B
Explanation:

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

SI unit of heat capacity is

  1. joule

  2. joule/kilogram

  3. joule/(kilogram x kelvin)

  4. joule/kelvin


Correct Option: D
Explanation:

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 temperatureThe SI unit for heat capacity of an object is joule per kelvin ($J/K$ or $J k^{-1}$).

Joule -second is the unit of

  1. Work

  2. Momentum

  3. Pressure

  4. Angular Momentum


Correct Option: D

A physical quantity u is given by the relation $u=\dfrac{B^2}{2\mu _0}$
Here, $B=$ magnetic field strength
$\mu _o=$ magnetic permeability of vacuum
The name of physical quantity u is?

  1. Energy

  2. Energy density

  3. Pressure

  4. None of these


Correct Option: B

Match the columns :

I II
1. Mass a. $m/s^2$
2. Weight b. kilogram
3. Gravitational acceleration c. $Nm^2\,\,kg^{-2}$
4. Gravitational constant d. Newton 

 

  1. 1-a ,2-b ,3-c ,4-d

  2. 1-b ,2-a ,3-d ,4-c

  3. 1-b ,2-d ,3-c ,4-a

  4. 1-b ,2-d ,3-a ,4-c


Correct Option: D
Explanation:

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

The SI units of mass and weight are ______

  1. kg and kg

  2. N and kg

  3. kg and N

  4. N and N


Correct Option: C
Explanation:

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.

Name the physical quantities related to the following units km$^2$

  1. Mass

  2. Volume

  3. Length

  4. Area


Correct Option: D
Explanation:

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 ${ km }^ { 2 }$.

How watt is related to the fundamental units?

  1. kg m$^2 s^{-3}$

  2. kg m$^2 s^{-2}$

  3. Nm $s^{-1}$

  4. Nm


Correct Option: A
Explanation:

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

Now power is defined as $=$ force $\times  $ velocity, where $F=m\times a$
So, $P=m\times a\times v$ , putting the SI unit of $m, a, v$
We get SI unit of power is $kgm^2s^{-3}$.

Which pair of following quantities has dimensions different from each other. 

  1. Impulse and linear momentum

  2. Planck's constant and angular momentum

  3. Moment of inertia and moment to force

  4. Young's modulus and pressure


Correct Option: C
Explanation:

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] $


Moment of force $=$ torque $= N.m = $$\left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ -2 } \right] $

Both are different from each other.

$\displaystyle { g\ cm\ s }^{ -2 }$ is also known as 

  1. newton

  2. erg

  3. pascal

  4. dyne


Correct Option: D
Explanation:

CGS unit of force is dyne.

$F=mg$, CGS unit of mass is gram  and gravity is $cm/s^2$ 
So, unit of dyne is $gcms^{-2}$.

In the SI system, the unit of P.E. is

  1. Erg

  2. Dyne-cm

  3. J

  4. Watt


Correct Option: C
Explanation:

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

Identify the uncommon quantity

Weight, spring balance, newton, kilogram 

  1. kilogram

  2. Weight

  3. spring balance

  4. newton


Correct Option: A
Explanation:

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.


Therefore, spring balance, weight and Newton are related to the same thing i.e.the weight of a body whereas the kilogram is related to the mass of the body. So, kilogram is different.

Identify the common unit used to measure energy?

  1. Newtons

  2. Joules

  3. Grams

  4. Meters

  5. Liters


Correct Option: B
Explanation:

Newton is the unit of force.

Joules is the SI unit of energy. It is equivalent to newton-meter($N-m$).
Grams is a unit of mass.
Meter is the SI unit of distance.
A liter is a unit of volume and equivalent to $dm^3$.

Therefore option $B$ is correct.

Volume is a derived quantity of length. True or false

  1. True

  2. False


Correct Option: A
Explanation:
Volume is calculated by the multiplying length, breadth and height.
Volume  $V = l\times b\times h$
Thus volume is a derived quantity.

Identify the derived quantities among the following.

  1. Gravitational constant

  2. Frequency

  3. Electric charge

  4. Electric current


Correct Option: A,B,C
Explanation:

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.

Using dimensional analysis the resistivity in terms of fundamental constants $h, m _e, c, e, \varepsilon _o$ can be expressed as.

  1. $\displaystyle\frac{h}{\varepsilon _0m _ece^2}$

  2. $\displaystyle\frac{\varepsilon _0m _ece^2}{h}$

  3. $\displaystyle\frac{h^2}{m _ece^2}$

  4. $\displaystyle\frac{m _e\varepsilon _0}{ce^2}$


Correct Option: C
Explanation:

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

For plank constant  $h$  SI base units are $Kgm^2s^{-1}$.
For $e$  SI unit is $C$.
For $c$  SI unit is $ms^{-1}$.
For $m _e$ SI unit is $Kg$.
For $\varepsilon _o$ SI unit is $C^2{Kg}^{-1}m^{-3}s^{2}$
Solving the dimensions of constants in option $C$,
$\dfrac{({Kgm^2s^{-1}})^2}{Kgms^{-1}C^2}=Kgm^3s^{-1}C^{-2}$
We get the dimensions of resistivity hence option $C$ is correct.

1 kg f cm$^{-2}$ .................. Nm$^{-2}$ .

  1. $10^{3}$

  2. $10^{5}$

  3. $10^{4}$

  4. $10^{6}$


Correct Option: B
Explanation:
$1kgf$ is the amount of gravitational force acting on $1kg$ of a body.
$1\ kgf\ =\ 10\ N$

And  $1m =100cm$ , 
so $1 kgf/cm^2 = 10\times10^4\ N/m^2$

we will get $10^5\ N/m^2$

Which of the following quantities has its unit as newton second?

  1. Energy

  2. Torque

  3. Momentum

  4. Angular momentum


Correct Option: C
Explanation:

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

$=\left[ { MLT }^{ -1 } \right] $
Dimensional formula of momentum $=\left[ { MLT }^{ -1 } \right] $
Hence, momentum has the unit as $Nsec$.

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