Question

If "g" denotes acceleration due to gravity and "G" denotes gravitational constant then g/G
yields the dimension​

Answer 1

Given:

'g' denotes Gravitational Acceleration, 'G' is Gravitational Constant.

To find:

Dimension of g/G ?

Calculation:

$\therefore \bigg \{ \dfrac{g}{G} \bigg \}$

$= \bigg \{ \dfrac{{M}^{0} L{T}^{ - 2} }{ \bigg( \dfrac{f {d}^{2} }{ {m}^{2} } \bigg)} \bigg \}$

$= \bigg \{ \dfrac{{M}^{0} L{T}^{ - 2} }{ \bigg( \dfrac{ ML{T}^{ - 2} \times {L}^{2} }{ {M}^{2} } \bigg)} \bigg \}$

$= \bigg \{ \dfrac{{M}^{0} L{T}^{ - 2} }{ \bigg( \dfrac{ M{L}^{3} {T}^{ - 2} }{ {M}^{2} } \bigg)} \bigg \}$

$= \bigg \{ \dfrac{{M}^{0} L{T}^{ - 2} }{ {M}^{ - 1} {L}^{3} {T}^{ - 2} } \bigg \}$

$= \bigg \{{M}^{1} {L}^{ - 2} {T}^{ 0}\bigg \}$

So, final answer is:

$\boxed{ \bf \dfrac{g}{G} = \bigg \{{M}^{1} {L}^{ - 2} {T}^{ 0}\bigg \}}$