Question

RELATIONSHIP BETWEEN SMALL g AND CAPITAL G

Answer 1

G is the universal sign and it is a constant value which means it cannot be changed whereas g is a variable and it can be changed

Answer 2

⚘ Answer :-

☯︎Relationship between small g and capital G:-

A free fall body of mass m and from a distance R from the centre of the earth of mass M. Then the gravitational force between the earth and the body is :-

$\red{ F = \dfrac{ \rm \: GMm}{R²}} \: ......(1)$

⚘ According to Newton's second law of motion:-

$\rm \: force = mass \times acceleration \: due \: to \: gravity$

$\red{ \rm \: f = m \times {G}}.........(2)$

❥ From equation (1) and (2)

$\large\rm \cancel{m} \times g = \frac{GM \cancel{m}}{R^{2} }$

$\bf \dag \underline {\boxed{ \bf \purple{ g = \frac{GM}{R {}^{2}} }}}$

where,

• ⪼ G = 6.67 × 10 -¹¹ Nm²/Kg²
• ⪼ m = 6 × 16²⁴ kg
• ⪼ R = 6.4 × 10⁶ m
• ⪼ g = 9.8 m/sec²

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