Question

If the velocity of light (C), the charge of the electron (e), time (T), and the universal gravitational constant (G) were taken as the ‘base ‘units’, the dimensions of ‘moment of inertia’ and electrical potential (V) would be

(1) [GC^-5T³] and [G^-1C^-5Te^-1], respectively

(2) [G^-1C⁵T³] and [G^-1C⁵Te^-1], respectively

(3) [GC^-5T^-3] and [GC^-5Te], respectively

(4) [G^-1C^-5T³] and [GC⁵T^-1e], respectively

Answer 1

(2) [G^-1C⁵T³] and [G^-1C⁵Te^-1], respectively

We have,

[C] = [LT^-1]

[e] = [lT]

[G] = [M^-1L³T^-2]

∴ [T] = [eT^-1]

[L] = [CT]

and [M] = [G^-1L³T^-2]

∴ [Moment of inertia] = [ML²]

= [G^-1L³t^-2L²] = [G^-1L⁵T^-2]

= [G^-1C⁵T⁵T^-2] = [G^-1C⁵T³]

and [Electrical potential] = [V] = (work/change)

= \([\frac{ML^2T^{-2}}{IT}]\)

= \([\frac{(G^{-1}C^3T^{-2})(c^2T^2)T^{-2}}{e}]\)

[G^-1C⁵Te^-1]