What are the dimensions and units of gravitational constant G in the formula 

F = G`\frac {m₁m₂}{r^2}` 

(Ans: [M⁻¹L³T⁻²], Nm² kg⁻²)

Given:

F = G`\frac {m₁m₂}{r^2}`


To Find:

Dimensions of G  = ?
Units of G  = ?


Solution:

As given 

F = G`\frac {m₁m₂}{r^2}`   

To Find G from the above formula, we have

G  = F`\frac {r^2}{m₁m₂}`   -------Equation (1)

dimensionally we have


as  [F] = [MLT⁻²], we have


or

[ G ] = [M⁻¹L³T⁻²]

Unit of G:

Using equation (1)

G  = F`\frac {r^2}{m₁m₂}` 

by Putting units of all quantities we have

G  = N`\frac {m^2}{kgｘkg}` 

G  = N`\frac {m^2}{kg^2}` 

or 

G  = Nm²kg⁻² --------Ans

thus, the unit of G is Nm²kg⁻² 

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Numerical Problem 1.6
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List of 11th Physics Numerical Problems of Chapter - 1
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