Tag: measurements and units

Questions Related to measurements and 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.

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

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

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

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

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

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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?

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

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

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

  3. ${ }{ V C } $

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

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Correct Option: C

The unit of Stefans constant $\sigma$ is:

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

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

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

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

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

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Correct Option: C

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

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

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

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

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

  4. Both and (b) and (c)

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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

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

  1. $pascal$

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

  3. $N / m ^ { 2 }$

  4. $k g , m$

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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

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

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

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

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

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

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Correct Option: D

The value of Faraday number in SI unit is:

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

  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 $

Show answer
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

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

  1. joule

  2. joule/kilogram

  3. joule/(kilogram x kelvin)

  4. joule/kelvin

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

The unit of power is

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

  1. Newton

  2. Joule

  3. Watt

  4. Newton meter

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Correct Option: C

Joule -second is the unit of

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

  1. Work

  2. Momentum

  3. Pressure

  4. Angular Momentum

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Correct Option: D