1.

In a new system of units energy, density and power are taken as fundamental units, then the dimensional formula of universal gravitational constant G will beWITH ALL THE STEPS OF THE SOLUTION

Answer»

Hello friend...!!!

⇒ the dimensional formula of gravitational constant : [M⁻¹L³T⁻²]

⇒ the dimensional unit of energy(E) : [ML²T⁻²]

⇒ the dimensional unit of density(D): [ ML⁻³]

⇒ the dimensional unit of power(P) : [ML²T⁻³]

now,

G = E^{a} X D^{b} x P^{<klux>N</klux>}

[M⁻¹L³T⁻²]  = [ML²T⁻²]ᵃ x [ ML⁻³]ᵇ x [ML²T⁻³]ⁿ

⇒ [M⁻¹L³T⁻²] = M⁽ᵃ ⁺ ᵇ ⁺ ⁿ ⁾  x L⁽²ᵃ ⁻³ᵇ ⁺²ⁿ⁾ x T⁽⁻²ᵃ ⁻³ⁿ ⁾

comparing both LHS and RHS , we get ,

a + b + n = -1 

2A -3b +2n = 3 

-2a - 3n = -2

by solving these three linear equations we get ,

a = -2 and b = -1 and n = 2

therefore ,

G = E^{a} x D^{b} x P^{n}

implies ,

G =[ E⁻²D⁻¹P²]

G = [ \frac{P^{2} }{ E^{2} D} ]


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hope it helps...!!!


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