Find the dimensions of 

(a) planck's constant 'h' from formula E = hf Where E is the energy and f is frequency. 

(b) gravitational constant 'G' from the formula F = G `frac {m₁m₂}{r^2}`. Where 'F' is force, 'm₁' and 'm₂' are masses of objects and 'r' is the distance between centers of objects. 

(a) [ML²T⁻¹] (b)[M⁻¹L³T⁻²]

Given:

(a) E = hf , Where E = energy and f = frequency. 

(b) F = G `frac {m₁₂m₂}{r^2}`. Where 'F' = force, 'm₁' and 'm₂' are masses of objects and 'r' = distance between centers of objects. 

To Find:


(a) dimensions of Planck's constant 'h' from formula E = hf 

(b) dimensions of Gravitational constant `\G` from the formula 

F =  `frac {Gm₁₂m₂}{r^2}`.


Solution:

(a) dimensions of Planck's constant 'h' from formula E = hf 

or

h = `\frac {E}{f}`

we have 

Dimensions of  [E] = [ML²T⁻²]

Dimensions of frequency [f]=[ T⁻¹]

therefore

h = `\frac {[ML²T⁻²]}{[ T⁻¹]}`

h = [ML²T⁻¹] ------Ans

Thus the dimension of Planck's constant h is [ML²T⁻¹]

(b) dimensions of Gravitational constant 'G' from the formula 


F =  `frac {Gm₁m₂}{r^2}`.

To Find `\G` from the above formula, we have

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

Dimensionally we can write as


as  [F] = [MLT⁻²], [m] = [M] and [t] = [T], So we have


or

[ `\G` ] = [M⁻¹L³T⁻²] --------Ans.

Thus the dimension of a gravitational constant G is [M⁻¹L³T⁻²]

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