Question

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 be

Answer 1

according to newton`s law of gravitation,
force = G×mass²/distance²
so G = (force×(distance²))/(mass²)
dimensional formula of G ={( MLT⁻²)×L²}/M² = M⁻¹L³T⁻²
dimensional formula of energy(E) = ML²T⁻²
dimensional formula of density(D) = ML⁻³
dimensional formula of power (P) = ML²T⁻³
  SO dimensional formula of G in terms of E,D,P will b = D⁻¹P²E⁻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 ]