Physics

# A physical quantity of the dimension of length that can be formed out of c, G and $\frac{e^{2}}{4\pi \epsilon _{0}}$ is [c is velocity of light, G is universal constant of gravitation and e is charge]

##### SOLUTION
Given,

$C,G,\dfrac{e^2}{4\pi \varepsilon_0}$

So,

$[L]=[C]^a,[G]^b[\dfrac{e^2}{4\pi \varepsilon_0}]^c$

$[L]=[LT^{-1}]^a,[ML^3T^{-2}]^b[ML^3T^{-2}]^c$

$[L]=L^{a+3b+3c}M^{-b+c}T^{-a-2b-2c}$

on comparing we get,

$a=3b+3c=1,$

$-b+c=0$

$a+2b+2c=0$

On solving we get,

$a=-2,b=\dfrac{1}{2},c=\dfrac{1}{2}$

Thus,

$L=\dfrac{1}{C^2}\sqrt{[\dfrac{Ge^2}{4\pi\varepsilon_0}]}$

You're just one step away

Subjective Medium Published on 18th 08, 2020
Questions 244531
Subjects 8
Chapters 125
Enrolled Students 202

#### Realted Questions

Q1 Single Correct Medium
If $L$ denotes the inductance of an inductor through which a current $i$ is flowing, the dimensions of $Li^2$ are
• A. $[ML^2T^{-2}]$
• B. $[MLT^{-2}]$
• C. $[M^2L^2T^{-2}]$
• D. not expressible in $M, L, T$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q2 Single Correct Medium
The dimensions of pressure are
• A. $MLT^{-2}$
• B. $ML^{-2}T^{2}$
• C. $ML^{-1}T^{-2}$
• D. $MLT^{2}$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q3 Single Correct Medium
Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is p. The viscosity of oil is given $\displaystyle \eta = \frac{p(r^2 - x^2)}{4vl}$, where v is velocity of oil at a distance x from the axis of the tube. The dimensional formula of viscosity is
• A. $[M^0 L^0 T^0]$
• B. $[M^1 L^{-1} T^{-1}]$
• C. $[M L^2 T^{-1}]$
• D. $[M^{-1} L^{-1} T^1]$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q4 Single Correct Medium
The workdone by a battery is $W=\varepsilon \Delta q$, where $\Delta q=$ charge transferred by battery, $\varepsilon =$ emf of the battery. What are dimensions of emf of battery?
• A. $[M^0L^0T^{-2}A^{-2}]$
• B. $[ML^2T^{-3}A^{-2}]$
• C. $[M^2T^{-3}A^0]$
• D. $[ML^2T^{-3}A^{-1}]$

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020

Q5 Single Correct Easy
Identify which of the following quantities is a scalar quantity?
• A. displacement
• B. mass
• C. resultant
• D. equilibrant
• E. 101 m/s at 30$^o$ north of east

Asked in: Physics - Units and Measurement

1 Verified Answer | Published on 18th 08, 2020