Question

hey mate,

the value of f on the surface of the earth is 9.8m s-2. the earth is taken to be a sphere of radius 6380 km, then estimate nthe mass of the earth.
G= 6.7×10-11 N M2 kg-2

Answer 1

hey mate,

here,
$g = 9.8m \: {s}^{2}$
G =
$6.7 \times {10}^{ - 11} n \: {m}^{2} {kg}^{ - 2}$
are radius of the earth,

R = 6380 km = 6380×1000m


$= \:6.38 \times { {10}^{6} }m$
g = GM/R2

hence, mass of the earth, M = gR2/G

$= \frac{9.8 \times 6.38 \times {10}^{6} }{(6.7 \times {10}^{ - 11} ) } \\ = 5.95 \times {10}^{24} kg$
I hope this helps you!
@vaibhav246