Question

In a new system of units Energy(E),density(d) and Power(P) are taken as the fundamental units then the dimensional formula of universal gravitational constant will be

Answer 1

The formula for gravitational constant -
g=F/M


Gravitational Field Intensity or Gravitational Strength at a point is defined as the gravitational force exerted on a unit mass placed at that point.

Mathematically,



Gravitational Field Intensity or Gravitational Strength = GM /r2
where G = Gravitational Constant, M = mass and r = distance from the centre of the body to the point.

Dimensional Formula of Universal Constant of Gravitation = M-1L3T-2
Dimensional Formula of Mass = M1L0T0
Dimensional Formula of Radius = M0L1T0

Substituting in the above equation we get,
Dimensional Formula of Gravitational Field Intensity or Gravitational Strength = M0L1T-2
SI unit of Gravitational Field Intensity or Gravitational Strength is N kg-1 or it can also be written as m s-1

Note: Gravitational Field Intensity is often referred as Gravitational Field.

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 ]