Question

In a new system of units energy (E) density (d) and power(p) are take as fundamental units then the dimensional formulae if gravirational constant G will be

Answer 1

G= Fd²/ Mm

Dimensional formula = [ML][L]²/[T]²[M]²
= [L]³/M[T]²
Dimensions of E,D & P
E= [ML²]/[T]²
P = [ML²]/[T]³
D= [M]/[L]³

So, the dimensional formula for G in terms of E,D & P will be
G= [P]²[D]/ [E]²

Answer 2

Answer:

G = E⁻²  D⁻¹  P²

Explanation:

E = [ M  L²  T⁻² ]

P = [ M  L²  T⁻³ ]

D = [ M  L⁻³  T⁰ ]

G = Nm²/Kg²  => [ M⁻¹  L³  T⁻² ]

G = Eᵃ  Dᵇ  Pˣ

Put values of E, D, P

G = [ M  L²  T⁻² ]ᵃ  [ M  L⁻³ ]ᵇ  [ M  L²  T⁻³ ]ˣ

G = [ Mᵃ⁺ᵇ⁺ˣ  L²ᵃ⁻³ᵇ⁺²ˣ  T⁻²ᵃ⁻³ˣ ]

COMPARE

a + b + x = -1

2a - 3b + 2x = 3

-2a -3x = -2

a = -2

b = -1

x = 2

G = [ E⁻²  D⁻¹  P² ]