Physics

# Consider the following two statements A and B. Identify the correct answer.A) The quantity $\dfrac { { e }^{ 2 } }{ { \epsilon }_{ 0 }ch }$ is dimensionless.B) $\dfrac { 1 }{ \sqrt { { \mu }_{ 0 }{ \epsilon }_{ 0 } } }$ has the dimensions of velocity and is numerically equal of velocity of light.

Both A and B are true

##### SOLUTION
Dimensions of permittivity ${ \epsilon }_{ 0 }$: ${ A }^{ 2 }{ T }^{ 4 }{ M }^{ -1 }{ L }^{ 3 }$
Dimensions of ${ e }^{ 2 }$ : ${ A }^{ 2 }{ T }^{ 2 }$
Dimensions of $c$ : $L{ T }^{ -1 }$
Dimensions of $h$ : $M{ L }^{ 2 }{ T }^{ -1 }$
Therefore, dimensions of the given expression:
$\dfrac { { A }^{ 2 }{ T }^{ 2 } }{ ({ A }^{ 2 }{ T }^{ 4 }{ M }^{ -1 }{ L }^{ 3 })\times (L{ T }^{ -1 })\times (M{ L }^{ 2 }{ T }^{ -1 }) } =1$ which is dimensionless.

Hence, Statement A is true.
In statement B, the expression given is for the speed of light.Hence, it has dimensions of velocity.

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!

Single Correct Medium Published on 18th 08, 2020
Questions 244531
Subjects 8
Chapters 125
Enrolled Students 197

#### Realted Questions

Q1 Single Correct Hard
If error in measuring the distance of a planet from sun is 0.4% and in measuring the mass of sun is 0.6% , then error in measuring the time period of planet around the sun is
• A. 1.8%
• B. 0.6%
• C. 1%
• D. 0.9%

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q2 Single Correct Medium
In ohm's law exp., reading of voltmeter across the resistor is 12.5 V and reading of current i = 0.20 Amp. Estimate the resistance in correct significant figure.
• A. 62 ohm
• B. 31 ohm
• C. 63 ohm
• D. 60 ohm

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q3 Single Correct Medium
A physical quantity, $y = \dfrac {a^4b^2}{(cd^4)^{1/3}}$ has four quantities $a, b, c$ and $d$. The percentage error in each quantity are $2\%, 3\%, 4\%$ and $5\%$ respectively. The error in $y$ will be:
• A. $6\%$
• B. $11\%$
• C. $12\%$
• D. $22\%$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q4 Single Correct Medium
If 1 g cm$^{-3} = 10^3\,kg\, m^{-3}$ then $10^6kgm^{-3}=$
• A. $10^{-3}\,g\,cm^{-3}$
• B. $10^{6}\,g\,cm^{-3}$
• C. $10^{3}\,g\,cm^{-3}$
• D. $10^{-6}\,g\,cm^{-3}$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q5 Single Correct Medium
1 $\mathring{A}$ is equal to :
• A. $0.1$ nm
• B. $10^{-10}$ cm
• C. $10^{-8} m$
• D. $10^{-4} \mu$.

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020