Tag: measurements and units

Quizzes (10) Questions (257)

Questions Related to measurements and units

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

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. $M^{-1}L^1T^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
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, 

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

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

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

$\implies \beta=[M^0L^2T^0]$
Multiple choice physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

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. $\dfrac{joule}{{m}^{2}{K}^{4}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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).

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

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)
Reveal answer Fill a bubble to check yourself
D Correct answer
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.


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

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. $\cfrac { \text { weber } } { \text { ampere-meter } }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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).

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

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 $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

SI unit of heat capacity is

  1. joule

  2. joule/kilogram

  3. joule/(kilogram x kelvin)

  4. joule/kelvin
Reveal answer Fill a bubble to check yourself
D Correct answer
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 temperature. The SI unit for heat capacity of an object is joule per kelvin ($J/K$ or $J k^{-1}$).