Question

what is the derivation of SI unit of G ??
plz answer it in mathematical derivation without any spam . If done it will be reported.​

Answer 1

Explanation:

We know that g= GM/r^2

Also, SI unit of-

g=m/s^2,M=kg,r=m

⇒ SI unit of G=(m/s^2)(m) 2/kg=[(kg)(m/s^2)](m)

2/kg 2=Nm2

/kg^2

Answer 2

TO FIND:

• What is the derivation of S.I. unit of Universal gravitation constant (G) ?

DERIVATION:

❒ Newton's Universal law of gravitation ➝ It states that ❝ Every particle in the universe attracts every other particle with a force which is directly proportional to the square of the distance between them. ❞

Thus, if m and m' are the masses of the two bodies separated by a distance d, then force of attraction F between them is given by:

$\rm{\dashrightarrow F \propto m \: m'}$

and

$\rm{\dashrightarrow F \propto \dfrac{1}{d^2} }$

$\rm{\dashrightarrow F \propto \dfrac{m \: m'}{d^2} }$

$\bf{\dashrightarrow F = G\dfrac{m\: m'}{d^2} }$

Where, G is a constant known as Universal gravitation constant.

If, m = m' = 1 kg

and

d = 1 m

then,

$\rm{\dashrightarrow Unit \: of \: G = \dfrac{F \: d^2}{m \: m'}}$

$\rm{\dashrightarrow \dfrac{F \times (1m)^2}{1kg \times 1kg}}$

$\rm{\dashrightarrow \dfrac{N \: m^2}{kg^2} }$ (Unit of force is Newton N)

$\bf{\dashrightarrow Unit \: of \: G = \dfrac{N \: m^2}{kg^2} \: or \: Nm^2 \: {kg}^{-2} }$

❝ Hence, the S.I. unit of G is Nm²/kg² ❞

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