Question

if G is universal gravitational constant and g is acceleratiob due to gravity then the unit of the quantity G/g i​

Answer 1

Answer:

Given:

G => Universal Gravitational constant

g => gravitational acceleration

To find:

Unit of the Quantity (G/g)

Calculation:

As per derivation from Newton's Law of Gravitation , we can say that :

$g = G \bigg \{\dfrac{m1 }{ {r}^{2} } \bigg \}$

Transposing Quantities to required sides :

$\implies \dfrac{G}{g} = \dfrac{ {r}^{2} }{m1}$

Unit of LHS will be same the unit of RHS.

Considering SI unit of all Quantities on the RHS , we can say that :

Unit of G/g will be :

$\implies \bigg \{\dfrac{G}{g} \bigg \} = \dfrac{ {(metre)}^{2} }{ (kg) }$

$\implies \bigg \{\dfrac{G}{g} \bigg \} = {(metre)}^{2} {(kg)}^{ - 1}$

So final answer is :

$\boxed{ \green{ \sf{ \large{ \bigg \{\dfrac{G}{g} \bigg \} = {(metre)}^{2} {(kg)}^{ - 1}}}}}$