Find the dimension of gravitational constant …
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Posted by Mayank Vekariya 5 years, 2 months ago
- 2 answers
Gaurav Seth 5 years, 2 months ago
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.
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Vanshika Kumari 5 years, 2 months ago
1Thank You