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What is the mass of earth from the following given data: Radius of earth $r = 6.37 \times 1 0^{6} m$ , acceleration due to gravity $g = 9.8 m / s^{2}$ and gravitational constant $G = 6.6 \times 1 0^{- 11} N m^{2} / k g^{2}$ .

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6 \times 1 0^{24} kg

6 \times 1 0^{14} kg

6 \times 1 0^{34} kg

6 \times 1 0^{12} kg

answer is A.

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Detailed Solution

The mass of the earth is

6 \times 1 0^{24} kg

.
Given ,
Radius of earth,

r = 6.37 \times 1 0^{6} m

Acceleration due to gravity,

g = 9.8 m / s^{2}

Gravitational constant,

G = 6.6 \times 1 0^{- 11} N m^{2} / k g^{2}

We know that,

g = \frac{GM}{r^{2}}

where

g

G

M

and

r

are the gravitational acceleration, gravitational constant, mass of the object and the radius of the object.
On substituting the values, we get

M = \frac{9.8 \times 6.37 \times 6.37 \times 10^{12}}{6.6 \times 10^{- 11}}

\Rightarrow M = \frac{397.6536 \times 10^{23}}{6.6}

\Rightarrow M = 60.2505 \times 1 0^{23}

\Rightarrow M = 6 \times 1 0^{24} kg

Hence, the mass of the earth is

6 \times 1 0^{24} kg

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