Question

Find the dimensions of G.

Answer 1

From the given formula

G = 3g / (4 π R ρ)

Dimensions of
g = [L T⁻²] ………(∵ It’s acceleration)
R = [L] ………(∵ It’s Radius)
ρ = [M L⁻³] ………(∵ It’s Density, i.e mass/volume)

So,

Dimension of G is
G = [L T⁻²] / ([L] × [M L⁻³])
G = [M⁻¹ L³ T⁻²]

Answer 2

Solution :

We have Provided with the mean  density of the earth and we need to find the dimension of G (Gravitational Constant ) .

Given Formula  :

P = $\frac{3g}{4\pi RG}$

⇒ $G = \frac{3g}{4\pi RP}$

Question Understanding :

R = Radius of the Earth

G = Gravitational Constant

g = Acceleration due to Gravity

P = Density

Knowing the dimensions :

• Radius (R) is Length which is Represented by L .
• Density is Mass/volume ,

⇒Mass = M

⇒Volume = L *L * L Which is equal to L^3

⇒ M/L^3

⇒ML^-3

• Acceleration due to Gravity

Acceleration = Change in Velocity/Time

⇒ Displacement/Time/Time

⇒ L/T/T

⇒ LT^-2

Putting the value in the formula for required answer

⇒$\frac{LT^-2}{L*ML^-3}$

⇒$M^-1L^3T^-2$

Hence , Our Required Answer is -1 , 3 , -2 for M L T which is mass , length and time