Physics

# Find the dimensions of: (i) Power, (ii) Forces and (iii) Permittivity of vacuum $(\varepsilon_o)$

##### SOLUTION

(I).The formula of power is

Power $P=\dfrac{W}{t}$

Now, the dimension of power is

$P=\dfrac{M{{L}^{2}}{{T}^{-2}}}{T}$

$P=M{{L}^{2}}{{T}^{-3}}$

(II).The formula of force is

$F=ma$

The dimension of force is

$F=ML{{T}^{-2}}$

(III).The formula of permittivity is

$F=\dfrac{1}{4\pi {{\varepsilon }_{0}}}\dfrac{q}{{{d}^{2}}}$

${{\varepsilon }_{0}}=\dfrac{q}{F{{d}^{2}}}$

$4\pi$ is a unit less so on neglect

So, the dimension of permittivity is

${{\varepsilon }_{0}}=\dfrac{{{\left[ TA \right]}^{2}}}{\left[ ML{{T}^{-2}} \right]\left[ {{L}^{2}} \right]}$

${{\varepsilon }_{0}}={{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}$

You're just one step away

Subjective Medium Published on 18th 08, 2020
Questions 244531
Subjects 8
Chapters 125
Enrolled Students 203

#### Realted Questions

Q1 Single Correct Medium
Two students P and Q perform an experiment to verify Ohm's law for a conductor with resistance R. They use a current source and a voltmeter with least counts of $0.1$mA and $0.1$mV, respectively. The plots of the variation of voltage drop(V) across R with current(i) for both are shown. the statement which is most likely to be correct is?
• A. P has only random error(s)
• B. Q has only systematic error(s)
• C. Q has both random and systematic errors
• D. P has both random and systematic errors

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q2 Single Correct Medium
A student wishes to find the volume of a small, irregularly-shaped stone.
A ruler and a measuring cylinder containing some water area available. Which apparatus is needed?
• A. neither the ruler nor the measuring cylinder
• B. the measuring cylinder only
• C. the ruler and the measuring cylinder
• D. the ruler only

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q3 Subjective Medium
Check the correctness of the equation$F=mv^2/r$ where F is a force, m is mass, v is velocity and r is a radius.

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q4 Subjective Medium
Automobiles air bags are inflated with $N_{2}$ gas which is formed by the decomposition of solid sodium azide $(NaN_{3})$. The other product is $Na - metal$. Calculate the volume of $N_{2}$ gas at $27^{\circ}C$ and $756\ Torr$ formed by the decomposing of $125\ gm$ of sod azide.

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q5 Subjective Medium
Taking force,length and time to be the fundamental quantities .Find the direction,density,momentum and energy.

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020