Question

35. If Eo is permittivity of free space, e is charge of proton,
G is universal gravitational constant and m is mass
of a proton then the dimensional formula for
e²/4piEoGm²
(1) [M'L'T-3A-1]
(3) [M'LPT-3A-1]
(2) [M°L°T°Aº]
(4) [M-'L-3T4A?]​

Answer 1

Given info : ε₀ is permittivity of free space, e is charge of proton, G is gravitational constant and m is mass of proton.

To find : the dimensional formula for e²/4πε₀Gm² is...

solution : we know, Kappa constant, k = 1/4πε₀

so, e²/4πε₀Gm² = ke²/Gm²

now units of k = Nm²/C²

so dimensions of k = [MLT¯²][L²]/[A²T²]

dimensions of e² = [AT]² = [A²T²]

we know, units of G = Nm²/kg²

so dimensions of G = [MLT¯²][L²]/[M²]

now dimensions of m² = [M²]

now, dimensions of e²/4πε₀Gm²

= dimensions of ke²/Gm²

= ([MLT¯²][L²]/[A²T²])([A²T²])/([MLT¯²][L²]/[M²])([M²])

= [M⁰L⁰T⁰A⁰]

Therefore the dimensions of e²/4πε₀Gm² is [M⁰L⁰T⁰A⁰]. i.e., option (2) is correct choice.

Answer 2

Answer:

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