Tag: measurements and units

Questions Related to measurements and units

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

physics measurements and units kinds of units fundamental quantities standardized measurement

  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}$

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Correct Option: B

In $S = a + bt + ct^{2}, S$ is measured in metres and $t$ is seconds. The unit of $c$ is

physics measurements and units kinds of units fundamental quantities standardized measurement

  1. $ms^{-2}$

  2. $m$

  3. $m^{-1}$

  4. None

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Correct Option: A

If the volume of a cube is equal to its surface area in magnitude. Then the volume of the cube is? 

physics measurements and units kinds of units fundamental quantities standardized measurement

  1. $216$ unit

  2. $512$ unit

  3. $64$ unit

  4. None of these

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Correct Option: A
Explanation:

Let us take side of cube$=a$
then  $a^3=6a^2$
$\therefore a=6$
So volume of cube is:

$a^3=(6)^3=216$ units

In the eqn. $\left (P+\dfrac {a}{V^2}\right )(V-b)=$ constant, the unit of $a$ is

physics measurements and units kinds of units fundamental quantities standardized measurement

  1. $dyne\times cm^5$

  2. $dyne\times cm^4$

  3. $dyne/cm^3$

  4. $dyne\times cm^2$

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Correct Option: B
Explanation:

Units of both $P $ and $ \dfrac {a}{V^2}$ must be same.
So, $\dfrac {a}{V^2}=P$  $\implies   a=PV^2$ 

Since unit of $P$ is $dyne \ cm^{-2}$ and that of $V$ is $cm^3$.
$\therefore$ Unit of a is  $\dfrac {dyne}{cm^2}(cm^3)^2=dyne\times cm^4$

Unit of specific resistance is

physics measurements and units kinds of units fundamental quantities standardized measurement

  1. $\Omega/m^2$

  2. $\Omega m^3$

  3. $\Omega m$

  4. $\Omega/m$

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Correct Option: C
Explanation:

Specific resistance of a material is given by

$\rho =\displaystyle \frac {RA}{l}$

Substitute the unit in the above expression:
$\rho=\dfrac {\Omega.m^2}{m}=\Omega m$

Which of the following physical quantity is different form others ?

physics measurements and units kinds of units fundamental quantities standardized measurement

  1. Displacement

  2. Velocity

  3. Force

  4. Kinetic energy

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Correct Option: D
Explanation:

Displacement, force, and velocity are vector quantities as they require direction as well as the magnitude for their representation but the kinetic energy is a scalar quantity as it does not require direction for its representation.

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

physics measurements and units kinds of units fundamental quantities standardized measurement

  1. $\displaystyle {m} { kg }^{ 2 }{ K }^{ -1 }$

  2. $\displaystyle {m} ^{2} { kg }^{ 2 }{ T }^{ -1 }$

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

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

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Correct Option: C
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  $m^2s^{-2}K^{-1}$.

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.

physics measurements and units kinds of units fundamental quantities standardized measurement

  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. $i \rightarrow c., ii \rightarrow c.,b., iii \rightarrow c.,d., iv \rightarrow c.,d.,$

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Correct Option: B

Which of the following units is a unit of power?

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. Kilowatt hour

  2. Watt

  3. Erg

  4. Calorie

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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.

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. calorie

  2. kilowatt hour

  3. joule

  4. watt

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Correct Option: D
Explanation:

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