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Physical quantities - class-XI

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Metre is the SI unit of

  1. mass

  2. volume

  3. length

  4. area


Correct Option: C
Explanation:

Metre is the SI unit of length.

Pressure is a standard unit of time.

  1. True

  2. False


Correct Option: B
Explanation:

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

Quantity of matter contained in a body is ....................... .

  1. Mass

  2. density

  3. relative density

  4. Volume


Correct Option: A
Explanation:

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

Knot is a measure of:

  1. The speed of ship

  2. The curvature of spherical objects

  3. Solar radiation

  4. Intensity of earthquake shock.


Correct Option: A
Explanation:

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".

Hence, option A is correct.

Which one of the following does not have unit of force per unit area:

  1. $Stress$

  2. $Strain$

  3. $Youngs Modulus$

  4. $pressure$


Correct Option: B
Explanation:
  • Stress  is the force per unit area on a body that tries to cause a change in shape. It is measured by the SI unit is Pascal.

  • Strain is defined as the deformation produced in a solid due to stress. It is measured by calculating the ratio of the two lengths. As a result it does not have any unit.  

  • Force is measured by the product of mass and acceleration. Its SI unit is Newton.

  • Pressure is measured by force per unit area. Its SI unit is Pascal.

So correct answer is option (B).

The base quantity among the following is:

  1. Speed

  2. Weight

  3. Length

  4. Area


Correct Option: C
Explanation:

 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.

If $L = \left( {20 \pm 0.01} \right)m$ and $B = \left( {10 \pm 0.02} \right)m$ then $\dfrac{L}{B}$ is 

  1. $ \left( {2 \pm 0.03} \right)m$

  2. $ \left( {2 \pm 0.015} \right)m$

  3. $ \left( {2 \pm 0.01} \right)m$

  4. $ \left( {2 \pm 0.005} \right)m$


Correct Option: A
Explanation:

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

Take $l=20+0.01, B=10+0.02$
Then $\cfrac {l}{B}=\cfrac {20.01}{10.02}=1.997$
Taken $l= 20-0.01$, $B=10-0.02$
There $\cfrac {l}{B}=\cfrac {19.99}{9.98}=2.003$
$\therefore$ The answer is $(2\pm 0.003)m$ .

Gauss is the unit of -

  1. B

  2. H

  3. M

  4. I


Correct Option: A
Explanation:

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

Debye is a unit of

  1. rms velocity

  2. force

  3. specific gravity

  4. electric dipole moment


Correct Option: D
Explanation:

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 CGS unit of energy is the dye.

  1. True

  2. False


Correct Option: B
Explanation:

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

Which quantities are measured in the same unit?

  1. energy, power and work

  2. energy and power, but not work

  3. energy and work, but not power

  4. power and work, but not energy


Correct Option: C
Explanation:
Quantity             Dimension
Energy              $ML^2T^{-2}$
Work                  $ML^2T^{-2}$
Power                 $ML^2T^{-3}$

So, the dimension of energy and work is same but different to power.
Option (C) is correct.

Watt-hour measures

  1. current

  2. voltage

  3. power

  4. electric energy


Correct Option: D
Explanation:

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

Thus Watt-hour means Power x Time, which is energy.

Maxwell is the unit of

  1. magnetic susceptibility

  2. intensity of magnetisation

  3. magnetic flux

  4. magnetic permeability


Correct Option: C
Explanation:

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

Find out the odd one from the given options.

  1. $Calorie$

  2. $Joule$

  3. $Ampere$

  4. $Kelvin$


Correct Option: C
Explanation:

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

Read the following statements carefully and pick out the correct choice of answer.
A: Electromotive force is expressed in Newtons.
B: Electric intensity is expressed in ${ VC }^{ -1 }$.

  1. Both A and B are correct.

  2. Both A and B are wrong.

  3. A is correct but B is wrong.

  4. A is wrong but B is correct.


Correct Option: B
Explanation:

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.

It is not a force but voltage and its unit is volt.

Electric intensity at a point is defined as the force experienced per unit positive charge at a point placed in the electric field. 
Its unit is $Newton/Coloumb=NC^{-1}$

Both statements are wrong.

Read the following statements carefully and pick out the correct choice of answer.
A: Susceptibility is expressed as ${ Am }^{ -1 }$.
B: Magnetic flux is expressed 
${ JA }^{ -1 }$.

  1. A is correct but B is wrong.

  2. A is wrong but B is correct.

  3. Both A and B are wrong.

  4. Both A and B are correct.


Correct Option: B
Explanation:

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


Hence, option B is correct.

India adopted metric system of units in

  1. 1947

  2. 1950

  3. 1956

  4. 2000


Correct Option: C
Explanation:

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

  1. self inductance (or) mutual inductance

  2. e.m.f

  3. capacity

  4. conductivity


Correct Option: A
Explanation:

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.

SI units were introduced in

  1. 1960

  2. 1956

  3. 1947

  4. None of these


Correct Option: A
Explanation:

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.

$\displaystyle kg{ ms }^{ -1 }$ is the SI unit of 

  1. Impulse

  2. Force

  3. Angular velocity

  4. None of these


Correct Option: A
Explanation:

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

Velocity gradient is defined as "change in velocity per unit distance". Then its unit in F.P.S. system is ____ .

  1. $\displaystyle foot \ { s }^{ -1 }$

  2. $\displaystyle { s }^{ -1 }$

  3. $foot \ s$

  4. $pound \ s$


Correct Option: B
Explanation:

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

$Velocity\ gradient=\dfrac{\Delta v}{\Delta x}$

Using the respective dimensions of $v$ and $x$.
$Velocity\ gradient=\dfrac{[LT^{-1}]}{[L]}$

So, its unit will be $sec^{-1}$.

Light travels at maximum speed in-

  1. Air

  2. Water

  3. Vacuum

  4. None of these


Correct Option: C
Explanation:

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.

Kilogram, gram, newton
 The odd one among the above stated quantities is :-
  1. newton

  2. Kilogram

  3. gram

  4. None


Correct Option: A
Explanation:

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

What is the full form of S.I. in S.I. system?

  1. Standard initiative

  2. Sponsored initiative

  3. Standard international

  4. Sponsored international


Correct Option: C
Explanation:

S.I system (standard international system). 

In this system the units of mass, length and time are same, as that of M.K.S system. 
However, it is an enlarged system encompassing all fundamental units.

Standard of unit is reproducible.

  1. True

  2. False


Correct Option: A
Explanation:

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.

Hence, the given statement is true.

The unit of magnetic field is?

  1. Weber/m

  2. Weber$/m^2$

  3. Weber

  4. Weber $\times$ meter


Correct Option: B
Explanation:

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

SI Unit of intensity of light is: 

  1. Newton

  2. Kelvin

  3. Kilogram

  4. Candela


Correct Option: D
Explanation:

Candela is the SI unit of intensity of light.

Which of the Quantity consists of unit as kg-m/sec ?

  1. Speed

  2. Momentum

  3. Acceleration

  4. Impulse


Correct Option: B,D
Explanation:

1.  For Speed :

    $v = \dfrac{distance}{time} = m/sec$

2. For Momentum : 
   $P = m \times v$

   Units :  $kg - m/ sec$

3. For Acceleration :
    $a = \dfrac{\Delta v}{\Delta t}=m/{sec}^2$

4. For Impulse :
    $I =F\times \Delta t = \Delta p$
     Units : $N-sec  = (kg-m/{sec}^2) \times sec = kg-m/sec$

From above we can say that $Momentum$ and $Impulse$ have same unit as kg-m/sec.
      

What is the approximate diameter of human hair?

  1. $500$nm

  2. $5000$nm

  3. $50$nm

  4. $50000$nm


Correct Option: D
Explanation:

Diameter of human hair is $50000$nm.

The unit kg $m^2s^{-2}$ is associated with

  1. Work

  2. Kinetic energy

  3. Potential energy

  4. All of these


Correct Option: D
Explanation:

$kgm^2s^{-2}$ 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.

Unit of power in S.I. system is

  1. Watt

  2. Calorie

  3. Newton

  4. Ergs


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

The 'rad' is the correct unit used to report the measurement of

  1. the rate of decay of radioactive source

  2. the ability of a beam of gamma ray photons to produce ions in a target

  3. the energy delivered by radiation to a target

  4. the biological effect of radiation


Correct Option: D
Explanation:

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.

Which of the following statements below should be followed while using the symbol for a unit of a physical quantity?

  1. The symbol named after scientist should have capital letter.

  2. They take plural forms.

  3. They can be written in full.

  4. They should be written only in the agreed symbols.


Correct Option: A,C,D
Explanation:

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

2. They can be written in full 
3. They should be written only in the agreed symbols be used while using the symbol for a unit of a physical quantity. 
4. They cannot take plural forms.

In CGS system, units of density is 

  1. kg/m$^3$

  2. gm/m$^3$

  3. kg/c.c

  4. gm/c.c


Correct Option: D
Explanation:

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

Unit of heat in S. I. system

  1. Watt

  2. Newton/ Meter

  3. Ergs / Sec

  4. Joule


Correct Option: D
Explanation:

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

S.I. unit of heat: Joul, Joule is defined as the amount of energy exerted when a force of one newton is applied over a displacement of one meter.
Option D.

1 Kilocalorie $=$ ..................... joules.

  1. $4000$

  2. $5000$

  3. $4200$

  4. None of these


Correct Option: C
Explanation:

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.

Option C. 

Which of the following is not a characteristic of the standard unit?

  1. It should be of convenient size.

  2. It should change with respect to space and time.

  3. It should not be perishable.

  4. It should be easily reproducible.


Correct Option: B
Explanation:

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

In the SI system, the unit of temperature is:

  1. Degree centigrade

  2. Kelvin

  3. Degree celsius

  4. Degree Fahrenheit


Correct Option: B
Explanation:

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 dimensions of $\varepsilon _0\frac {d \Phi _E  }{  dt} $ is (where symbols has their usual meaning)

  1. $[AT]$

  2. ${A}$

  3. $[ML^2T^{-2}]$

  4. $[ML^{-2}T^{-2}]$


Correct Option: A

The measure of motion of a body is 

  1. Speed

  2. Velocity

  3. Momentum

  4. Inertia


Correct Option: C
Explanation:

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.

Unit of magnetic moment is

  1. Ampere-metre$^ { 2 }$

  2. Ampere-metre

  3. Weber-mettre$^ { 2 }$

  4. Weber/metre


Correct Option: A
Explanation:

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 :

  1. power

  2. energy

  3. quantity of electricity

  4. strength of current


Correct Option: C
Explanation:

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

Power is measured in Watt.
Energy is measured in Joules.
Strength of current ia measured in Amperes.

In S.I . system value of G is ......${ Nm }^{ 2 }/{ kg }^{ 2 }$ 

  1. $7.673\times 10^{ -11 }$

  2. $6.763\times 10^{ -11 }$

  3. $6.673\times 10^{ -11 }$

  4. $7.367\times 10^{ -11 }$


Correct Option: C

What is the  $SI$  unit of permeability?

  1. Henry per metre

  2. Tesla metre per ampere

  3. Weber per ampere metre

  4. All the above units are correct


Correct Option: D

The unit of ${Iq}{Z}$ is:

 $I=$Current, $Z= $Electrical Impedance and $q =$ Charge 

  1. Newton

  2. Dyne

  3. Joule

  4. None


Correct Option: C
Explanation:

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


Expression is $ { { I }^{ 2 } }{ Z } t$.

This is $Electrical\quad Power\quad X\quad time$. Hence the unit is $Joule$.

If E and H represent electric field and magnetic field intensity respectively, then E/H has unit of 

  1. Ampere

  2. Ohm

  3. Volt

  4. Joule


Correct Option: B

Express 100 K in $^0C$

  1. $ - {273^0}C$

  2. $ {100^0}C$

  3. $ {212^0}C$

  4. $ - {173^0}C$


Correct Option: C

Which of the following is not a unit of heat energy?

  1. Joule

  2. Kelvin

  3. Calorie

  4. None of these


Correct Option: B

Which of the following is not the unit of surface tension ? 

  1. $newton/meter$

  2. $joule/(meter)^2$

  3. $kg/(second)^2$

  4. $watt/ meter$


Correct Option: D

The Vander waal's equation for gas is given by $\left (P + \dfrac {a}{V^{2}}\right )(V - b) = RT$ where $P$ is pressure, $V$ is volume $'a'$ and $'b'$ are constants, $R$ is universal gas constant and $T$ is absolute temperature. Then the units of $'a'$ are

  1. $dyne\times cm^{5}$

  2. $dyne\times cm^{4}$

  3. $dyne\times cm^{3}$

  4. $dyne\times cm^{2}$


Correct Option: B

Acceleration is defined as the rate of change of velocity. Unit of rate of change of acceleration is:

  1. $m/s^{2}$

  2. $m/s^{3}$

  3. $m/s$

  4. $m^{2}/s^{3}$


Correct Option: B
Explanation:

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

The rate of change of acceleration $\dfrac { d\overset { \rightarrow  }{ a }  }{ dt } =\dfrac { { d }^{ 3 }y }{ d{ t }^{ 3 } } =\dfrac { m }{ { s }^{ 3 } } $
Hence, option B is correct.

To express all the physical quantities in SI units, we need 

  1. two fundamental units

  2. three fundamental units

  3. five fundamental units

  4. seven fundamental units


Correct Option: D
Explanation:

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.

Which of the following quantity is unitless ?

  1. Velocity gradient

  2. Pressure gradient

  3. Displacement gradient

  4. Force gradient


Correct Option: C
Explanation:

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.

In a system of units, the units of mass, length and time are called pail, jack, and jill. 1 pail = 5 kg, 1 m = 5 jacks and 24 s make 1 jill. What are the unit of density and speed in the new system?

  1. $\displaystyle { (pails)\quad (jills) }^{ -2 }$

  2. $\displaystyle { (pails)\quad (jack) }^{ -3 }$

  3. $\displaystyle { (jack) }^{ 2 }(jill)$

  4. $\displaystyle { (pails)\quad (jack) }^{ 2 }$


Correct Option: B
Explanation:

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

The value of $\displaystyle G=6.67\times { 10 }^{ -11 } N \ { m }^{ 2 } kg^{ -2 } and \ g={ 9.8ms }^{ -2 }$, what is the unit of g/G in C.G.S system?

  1. $\displaystyle { g\quad cm }^{ -2 }$

  2. $\displaystyle { g\quad cm }^{ 2 }$

  3. $\displaystyle { g\quad cm }^{ -1 }$

  4. $\displaystyle { g\quad cm }$


Correct Option: A
Explanation:
Unit of $g$ in SI is  $ms^{-1}$ and that of $G$ is $Nm^2 kg^{-2}$.
where  $1 \ N   = 1 \ kg \ ms^{-2}$ (in MKS system)

So, MKS units of $G$ is $m^3s^{-2}kg^{-1}$

Thus CGS unit of $g$ is  $cm \ s^{-2}$ and that of $G$ is $cm^3 s^{-2} g^{-1}$

Thus CGS unit of  $g/G$ is $g \ cm^{-2}$

The  SI unit of weight is.

  1. kg wt

  2. N

  3. g wt

  4. all the above


Correct Option: B
Explanation:

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 consists of

  1. a number and a unit

  2. a number

  3. a unit

  4. a unit and its symbol


Correct Option: B
Explanation:

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


Option $B$ is correct.

If kg $m^2s^2$ represents 'x' and g $cm^2s^2$ represents 'y', then find the ratio of x to y.

  1. 10$^7$

  2. 10$^5$

  3. 10$^9$

  4. 10$^3$


Correct Option: A
Explanation:

We know that, 

$1 kg=1000g$
$1m=100cm$

Now, converting the unit $kg\ m^2\ s^2$ into $g\ m^2\ s^2$

$1\ kg\ m^2\ s^2=1000\ g\times(100\ m)^2\ s^2$

$=1000\times10^4\ g\ m^2\ s^2$
$=10^7 g\ cm^2\ s^2$

Which of the following unit is different from other:

  1. Electron volt

  2. Kilo Watt hour

  3. Watt sec

  4. Volt


Correct Option: D
Explanation:
Electron volt, kilo Watt hour and Watt sec are the units of energy but volt is the unit of potential difference (or voltage).
Thus volt is odd one out here.

$Weber/{m^2}$ = 

  1. Tesla

  2. Dyne

  3. Watt

  4. Henry


Correct Option: A
Explanation:
$Weber/m^2$ is the S.I. unit of magnetic field strength. Magnetic field is also measured in another SI unit $Tesla$.
$Weber/m^2 = Tesla$

1 Nanometer = ?

  1. ${10^{-3}}m$

  2. ${10^{-6}}m$

  3. ${10^{-9}}m$

  4. ${10^{-12}}m$


Correct Option: C
Explanation:
According to the standard conversions,  $1 \ nm = 10^{-9}\ m$
One nanometer is vary small unit. of distance.

Accuracy of a measurement is determined by :

  1. Absolute

  2. Percentage

  3. Both

  4. None of these


Correct Option: B
Explanation:

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

65 mm is equivalent of approximately:

  1. 1.5 inches

  2. 3.5 inches

  3. 2.6 inches

  4. 10.5 inches


Correct Option: C
Explanation:

We know that $1 \ mm = 0.039 \ inch$ 


So  $65 \ mm = 65 \ mm\times \dfrac{0.039 \ inch}{1 \ mm} = 2.6 \ inches$

What is number of significant figures in $0.310\times 103$ ?

  1. 2

  2. 3

  3. 4

  4. 6


Correct Option: B
Explanation:

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.

One Femto is equal to :

  1. ${10^{15}}$

  2. ${10^{-15}}$

  3. ${10^{-12}}$

  4. ${10^{-10}}$


Correct Option: B
Explanation:
One Femto is a very small unit.
$1$ Femto $ = 10^{-15}$

SI unit of Angle is Steradian?

  1. True

  2. False


Correct Option: B
Explanation:

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.

Pascal is unit of which of the following quantity?

  1. Temperature

  2. Pressure

  3. Force

  4. Impulse


Correct Option: B
Explanation:

Pressure is measured in Pascal $(Pa)$.

Which of the two have same dimensions ?

  1. Force & Strain

  2. Angular velocity & Angular Frequency

  3. Force & Stress

  4. None of the above


Correct Option: B
Explanation:

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

Which of the following pairs of physical quantities have same dimensions?

  1. Force and power

  2. Torque and energy

  3. Torque and power

  4. Force and torque


Correct Option: B
Explanation:
Torque is the moment of force given by:$ \vec\tau=\vec r\times \vec F$

It’s unit is Newton-meter.

The unit of work/energy is also Newton-meter or Joule.

Thus, both of these physical quantities have the same units/dimensions.

$[Torque]=[M][L]^{2}[T]^{−2}=[Energy]$

Which one of the following is not a derived unit?

  1. joule

  2. watt

  3. kilogram

  4. newton


Correct Option: C
Explanation:

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

Which of the following statements is incorrect regarding mass. ?

  1. It is a basic property of matter.

  2. The SI unit of mass is kg.

  3. The mass of an atom is expressed in u.

  4. It depends upon the temperature, pressure or location of the object in space.


Correct Option: D
Explanation:

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

Which of the following is unitless quantity?

  1. Pressure gradient

  2. Displacement gradient

  3. Force gradient

  4. Velocity gradient


Correct Option: B
Explanation:

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:

  1. Is a unit of pressure

  2. Is a unit of force

  3. Gives an idea of the composition of air

  4. Is the height above which there is no atmosphere


Correct Option: A
Explanation:

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


So, it is a unit of pressure. Option $A$ is correct.

In a screw gauge, 5 complete motations of the screw cause it to a linear distance of 0.25 cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisiors and 30 circular scale divisions. Assuming negligible zero, the thickness of the wire is:

  1. $0.4300$ cm

  2. $0.2150$ cm

  3. $0.3150$ cm

  4. $0.0430$ cm


Correct Option: B
Explanation:
In one rotation, scale moves $\dfrac{0.25}{5}=0.05\,cm$

Least count $=0.05\times 10^{-2}\,cm$

For $4$main scale division $=4\times 0.05=0.2\,cm$

For circular scale division $30\times 0.05\times 10^{-2}=1.5\times 10^{-2}\,cm$

Thickness of wire $0.2+0.015=0.2150\,cm$

Assuming the length of the day uniformly increases by $0.001$ second per century. The net effect on the measure of time over $20$ centuries is?

  1. $3.2$ hour

  2. $2.1$ hour

  3. $2.4$ hour

  4. $5$ hour


Correct Option: B
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