Physics · Science General

Units and Measurement

1,044 Questions

Master the fundamentals of physics with these practice questions on units and measurement. The topics include fundamental SI units, derived quantities, and specific units for power, force, and light. These questions are essential for building a strong foundation for competitive exams.

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Units and Measurement Questions

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

The Sl unit of length is the meter. Suppose we adopt a new unit of length which equals to $x$ meters. The area 1 $m ^ { 2 }$ expressed in terms of the new unit has a magnitude:

  1. $x$
  2. $x ^ { 2 }$
  3. $\dfrac { 1 } { x }$
  4. $\dfrac { 1 } { x ^ { 2 } }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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 $     

$=\dfrac{1}{x^2}$     

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

If $10 ^ { 7 }$ era is taken as unit of energy, $10 ^ { 5 }$ dyne as the unit of force, one second as unit of time. what is, the unit of length?

  1. $1$ $m$
  2. $10$ $m$
  3. $100$ $m$

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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.

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

The MKS unit of quantity $\dfrac{\pi \eta r^4}{2}$ is :

  1. $N s {m}^{2} radian $
  2. $Ns/m/Radian$
  3. $Radian/Ns/m$
  4. $ Ns/m/Radian^2 $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Unit of $\pi $ is radians.

Unit of $r$ is $m$.
Unit of coefficient of viscosity, $\eta =N\, s\, { m }^{ -2 } $
Whereas $2$ is just a number, so it is unit less.
Therefore, Unit of given expression $=radian \times$ $N\, s\, { m }^{ -2 }\times { m }^{ 4 }=N\,s \, { m }^{ 2 } \ radian$

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

Unit of self inductance is

  1. $\cfrac { newton\ second }{ coulomb\quad \times \quad ampere } $
  2. $\cfrac { joule/coubmb\quad \times \quad second }{ ampere } $
  3. $\cfrac { volt\quad \times \quad metre }{ coulomb } $
  4. $\cfrac { newton\quad \times \quad metre }{ ampere } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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.

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

kilowatt-hour is the unit of ____. 

  1. potential difference

  2. electric power

  3. electric energy

  4. charge
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

As the power$(means $ $ \dfrac{Work}{time}=\dfrac{energy}{time})$
so $energy=power\times time $

$\text{so unit of energy= unit of power *unit of time =watt *second }$
Kilowatt-hour is just $3600\times 1000$ times  of the above value of energy.

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

The unit of permittivity of free space, $ \varepsilon _ o $ is

  1. $\dfrac {Coulomb} {newton - meter}$
  2. $ \dfrac {newton - meter^2} { Coulomb ^2} $
  3. $\dfrac {Coulomb^2}{newton- meter^2} $
  4. $ \dfrac {Coulomb^2} {(newton-metre)^2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From Coulomb's law, F = (1 / (4 pi epsilon_0)) * (q1 * q2 / r^2). Rearranging for epsilon_0 gives units of (Coulomb * Coulomb) / (newton * meter^2), which simplifies to Coulomb^2 / (newton * meter^2).

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

Write the SI unit of the physical quantity having following dimensional formula
$\displaystyle [{ M }^{ 0 }{ L }^{ 2 }{ T }^{ -2 }{ K }^{ -1 }]$.

  1. $\displaystyle {m} { kg }^{ 2 }{ K }^{ -1 }$
  2. $\displaystyle {m} ^{2} { kg }^{ 2 }{ T }^{ -1 }$
  3. $\displaystyle {m} ^{2} { s }^{ -2 }{ K }^{ -1 }$
  4. $\displaystyle {m} ^{2} { kg }^{ 2 }{ K }^{ -1 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
SI unit of $M$ is $kg$, that of $L$ is $m$, $T$ is $s$ and temperature (K) is $K$.

So, SI unit of $[M^0L^2T^{-2}K^{-1}]$ is  $m^2s^{-2}K^{-1}$.
Multiple choice physics measurement of physical quantities kinds of units fundamental quantities standardized measurement

A dimensionless quantity

  1. never has a unit

  2. always has unit

  3. may have a unit

  4. does not exit
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

But it is not necessary. A dimensionless quantity is unitless. And eg, for this, is radian (unit of angle), which is dimensionless quantity because it is the ratio of two lengths.

Multiple choice physics measurements and units kinds of units fundamental quantities standardized measurement

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II.

Column I Column II
i. $GM _eM _s$ a. (volt) (coulomb) (metre)
ii. $3RT/M$ b. $(kilogram)(metre)^3 (second)^2$
iii. $F^2/q^2B^2$ c. $(meter)^2 (second)^{-2}$
iv. $GM _e/R _e$ d. $(farad) (volt)^2 (kg)^{-1}$


where G is universal gravitational constant; $M _e$ mass of the earth; $M _s$, mass of sun; $R _e$ radius of the earth; R, universal gas constant;T, absolute temperature; M, molar mass, F, force; q, charge; B, magnetic field.

  1. $i \rightarrow b., ii \rightarrow c.,d., iii \rightarrow c.,d., iv \rightarrow c.,d.,$
  2. $i \rightarrow a., ii \rightarrow c.,d., iii \rightarrow c.,d., iv \rightarrow c.,d.,$
  3. $i \rightarrow d., ii \rightarrow c.,d., iii \rightarrow c.,d., iv \rightarrow c.,d.,$
  4. $i \rightarrow c., ii \rightarrow c.,b., iii \rightarrow c.,d., iv \rightarrow c.,d.,$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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.