Question

Define ‘g’ and ‘G’. Establish relation between the two. How do you use this relation to calculate mass of
earth ?

Answer 1

$\huge\rm\underline\purple{Question :-}$

Define ‘g’ and ‘G’. Establish relation between the two. How do you use this relation to calculate mass of earth ?

$\large{\underbrace{\sf{\red{ Required\:Answer :}}}}$

g = Acceleration due to gravity

= 9.8 m/${s\;^2}$

G = Universal Gravitational Constant

= 6.67 × ${10\;^-11}$ N${m\;^2}$/ ${kg\;^2}$

$\green{\underline\bold{Relation\: between \:'g'\: and\: 'G':}}$

${\large{\bold{\sf{\bf {\underline{From\: universal \:law \:of \:gravitation,}}}}}}$

F = $\frac{GMm}{R\;^2}$ ⟶ ( 1 )

${\large{\bold{\sf{\bf {\underline{From\: Newtons \:second \:law,}}}}}}$

F = mg ⟶ ( 2 )

$\purple{\underline\bold{From\: ( 1 ) \:and \:( 2 ). \:We \:get :}}$

⇒ mg = $\frac{GMm}{R\;^2}$

⇒ g = $\frac{GM}{R\;^2}$

$\blue{\underline\bold{Where,}}$

g = Acceleration due to gravity.

G = Universal Gravitational Constant.

R = Radius of the earth.

∴ Mass of the earth,m = $\frac{gR\;^2}{G}$

$\pink{\underline\bold{Where,}}$

R = 6400 km

g = 9.8 m/${s\;^2}$

G = 6.67 × ${10\;^-11}$ N${m\;^2}$/ ${kg\;^2}$

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