Physics

Dimensions of $\displaystyle \frac{1}{\mu_{0}{\varepsilon_{0}}}$ , where symbols have their usual meaning, are :

$[\mathrm{L}^{2}\mathrm{T}^{-2}]$

SOLUTION
Vaccum permittivity:
${ F }_{ c }=\dfrac { 1 }{ 4\pi { \varepsilon }_{ 0 } } \times \dfrac { { q }_{ 1 }{ q }_{ 2 } }{ { r }^{ 2 } }$
Where $\varepsilon_0$ is permttivity of vaccum.
Dimension will be $[M^{-1}L^{-3}T^{4}I^{2}]$

vaccum permeability:
${ \mu }_{ 0 }=4\pi \times { 10 }^{ -7 }\quad N/{ A }^{ 2 }$
Dimensions will be $[MLT^{-2}I^{-2}]$

Dimensions for $\dfrac { 1 }{ { \mu }_{ 0 }{ \varepsilon }_{ 0 } }$ will be $\dfrac { 1 }{ [{ M }^{ -1 }{ L }^{ -3 }{ T }^{ 4 }{ I }^{ 2 }]\times [{ M }^{ 1 }{ L }^{ 1 }{ T }^{ -2 }{ I }^{ -2 }] } =[L^2T^{-2}]$

You're just one step away

Single Correct Medium Published on 18th 08, 2020
Questions 244531
Subjects 8
Chapters 125
Enrolled Students 218

Realted Questions

Q1 Single Correct Medium
Least count of spring balance, if a spring balance has a range of $0-25\ kg$ and consists for every $kg$ increment in weight the needle moves by $10$ divisions?
• A. $100\ g/mm$
• B. $0.0001\ g/mm$
• C. $0.1\ g/cm$
• D. $1\ g/m$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q2 Single Correct Medium
The dimensional formula of couple is
• A. $[ML^{2}T^{-2}]$
• B. $[MLT^{-2}]$
• C. $[ML^{-1}T^{-3}]$
• D. $[ML^{-2}T^{-2}]$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q3 Assertion & Reason Medium
ASSERTION

The value of $1$ Micron is equal to $10^{-5}m$

REASON

Micron is the unit for measuring microscopic distance.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q4 Single Correct Medium
$V$ is the volume of a liquid flowing per second through a capillary tube of length $l$ and radius $r$, under a pressure difference $(p)$. If the velocity $(v)$, mass $(M)$ and time $(T)$ are taken as the fundamental quantities, then the dimensional formula for $\eta$ in the relation $V = \dfrac {\pi p r^{4}}{8\eta l}$ is
• A. $[MV^{-1}]$
• B. $M^{-1} V^{-1} T^{-2}]$
• C. $[M^{1}V^{1}T^{-2}]$
• D. $[M^{1}V^{-1}T^{-2}]$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q5 Single Correct Medium
The velocity $v$ of a particle at time$t$ is given by $\displaystyle v = at + \frac {b} {t + c}$ where $a, b$ and $c$ are constants. The dimensions of $a, b$ and $c$ are respectively :
• A. $LT^{-2}\, , L$ and $\displaystyle T$
• B. $L^{2}\, , T$ and $\displaystyle LT^{2}$
• C. $LT^{2}\, , LT$ and $\displaystyle L$
• D. $L\, , LT$ and $\displaystyle T^{2}$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020