Mass and Average Density of Earth

by • 04/07/2012 • GeneralComments (0)573

Mass and Average Density of Earth

Let,

M = Mass of an object placed near the surface of earth

M(e) = Mass of earth

R(e) = Radius of earth

G = Acceleration due to gravity

According to theNewton’s Law of Universal Gravitation.

F = G M Me / Re2 ……………………….. (1)

But the force with which earth attracts a body towards its centre is called weight of that body.

 

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Therefore,

F = W = Mg

(1) => M g = G M Me / Re2

g = G Me / Re2

Me = g Re2 / G ……………………………. (2)

Put

g = 9.8 m/sec2,

Re = 6.38 x 10(6) m,

G = 6.67 x 10(-11) N-m2/kg2, in equation (2)

(1) => Me = 5.98 x 10(24) kg. ………………. (In S.I system)

Me = 5.98 x 10(27) gm ……………………………… (In C.G.S system)

Me = 6.6 x 10(21) tons

For determining the average density of earth (ρ),

Let Ve be the volume of the earth.

We know that

Density = mass / volume

Therefore,

ρ = Me / Ve ……………………… [Ve = volume of earth]

ρ = Me / (4/3 Π Re3) ………….. [since Ve = 4/3 Π Re3]

ρ = 3 Me / 4 Π Re3

Put,

Me = 5.98 x 10(24) kg

& Re = 6.38 x 10(6) m

Therefore,

ρ = 5.52 x 10(3) kg / m3

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