give the value and dimension of gravity
Answers
Explanation:
The dimensional formula of gravitational constant is given by,
M-1 L3 T-2
Where,
M = Mass
L = Length
T = Time
Derivation
From Newton’s law of gravitation,
Force (F) = [GmM] × r-2
Gravitational Constant (G) = F × r2 × [Mm]-1 . . . . (1)
Since, Force (F) = Mass × Acceleration = M × [LT-2]
∴ The dimensional formula of force = M1 L1 T-2 . . . . (2)
On substituting equation (2) in equation (1) we get,
Gravitational Constant (G) = F × r2 × [Mm]-1
Or, G = [M1 L1 T-2] × [L]2 × [M]-2 = [M-1 L3 T-2].
Therefore, the gravitational constant is dimensionally represented as M-1 L3 T-2.
⇒ Check Other Dimensional Formulas:
Dimensions of Gravitational Potential Energy
Dimensions of Temperature
Dimensions of Linear Momentum
Dimensions of Boltzmann Constant
Dimensions of Permittivity
Answer:
Its value is 9.8 m/s^2 on Earth.
That is to say, the acceleration of gravity on the surface of the earth at sea level is 9.8 m/s^2.
Or,
G = [M^1 L^1 T^-2] × [L]^2 × [M]^-2 = [M^-1 L^3 T^-2].
Therefore, the gravitational constant is dimensionally represented as M^-1 L^3 T^-2