Question

v) Calculate the mass of the Earth if acceleration due to gravity g = 9.81 m/s? and
radius of Earth is 6.37 x 10 m.(G-6.67 x 10-11 Nm²/kg)​

Answer 1

Answer:

$\large\bold\red{Mass\:of\:Earth=6×{10}^{24}\:Kg}$

Explanation:

Given,

Acceleration due to gravity,

$g = 9.81=9.8 \: m {s}^{ - 2}$

Radius of earth,

$R = 6.37 \times {10}^{6} \: m \\ \\ = > R= 6.4 \times {10}^{6} \: m$

and,

Universal Gravitational Constant,

$G = 6.67 \times {10}^{ - 11} \: n {m}^{2} {kg}^{ - 2}$

Now,

Let ,

the mass of Earth be 'M'

But,

We know that,

$\large\bold{g = \frac{GM}{ {R}^{2} }}$

Therefore,

pUtting the values,

we get,

$= > 9.8 = \frac{6.67 \times {10}^{ - 11} \times m}{ {(6.4 \times {10}^{6}) }^{2} } \\ \\ = > m = \frac{9.8 \times {(6.4)}^{2} \times {10}^{12} }{6.67 \times {10}^{ - 11} } \\ \\ = > m = \frac{9.8 \times {(6.4)}^{2} \times {10}^{(12 + 11)} }{6.67} \\ \\ = > m = \frac{9.8 \times {(6.4)}^{2} \times {10}^{23} }{6.67}$

After simplification,

we get,

$\bold{M= 6 \times {10}^{24} \: Kg}$