From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is :

Question

From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is : (A) (ch/2πϵ20) (B) (e2/2πϵ0Gme2) (me = mass of electron) (C) (μ0 ϵ0/c2) (G/he2) (D) (2π√μ0ϵ0/ce2) (h/G)

Tardigrade Admin · Accepted Answer

A dimensionless unitless terms will have same value is all systems.

Q. From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is :

$\frac{c h}{2 π ϵ _{0}^{2}}$

$\frac{e ^{2}}{2 π ϵ _{0} G m _{e}^{2}}$ ( $m_{e}$ = mass of electron)

$\frac{μ _{0} ϵ _{0}}{c ^{2}} \frac{G}{h e ^{2}}$

$\frac{2 π μ _{0} ϵ _{0}}{c e ^{2}} \frac{h}{G}$

A dimensionless & unitless terms will have same value is all systems.

Q. From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is :

2πϵ02​ch​

2πϵ0​Gme2​e2​ (me​ = mass of electron)

c2μ0​ϵ0​​he2G​

ce22πμ0​ϵ0​​​Gh​

A dimensionless & unitless terms will have same value is all systems.

$\frac{c h}{2 π ϵ _{0}^{2}}$

$\frac{e ^{2}}{2 π ϵ _{0} G m _{e}^{2}}$ ( $m_{e}$ = mass of electron)

$\frac{μ _{0} ϵ _{0}}{c ^{2}} \frac{G}{h e ^{2}}$

$\frac{2 π μ _{0} ϵ _{0}}{c e ^{2}} \frac{h}{G}$