Question

Write the dimension of gravitationa constant and pressure​

Answer 1

`[M^(-1) L^(3) T^(-2)]`

Step-by-step explanation:

From Newton’s law of gravitation,

Force (F) = [GmM] ×
`r^(-2)`

Gravitational Constant (G) = F ×
`r^(2)` ×
`[Mm]^(-1)` . . . . (1)

Since, Force (F) = Mass × Acceleration = M ×
`[LT^(-2)]`

∴ The dimensional formula of force =
`M^(1) L^(1) T^(-2)` . . . . (2)

On substituting equation (2) in equation (1) we get,

Gravitational Constant (G) = F ×
`r^(2)`×
`[Mm]^(-1)`

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)`