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Q.

What will be the mass of the earth if the radius is given as:

Radius of earth $= 6.37 \times 10^{6} m^{}$

acceleration due to gravity $= 9.8 m / \sec^{2}$

gravitational constant $G = 6.6 \times 10^{- 11} N m^{2} / {kg}^{2}$

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a

6 \times 10^{24}

kg

b

6 \times 10^{14}

kg

c

6 \times 10^{20}

kg

d

6 \times 10^{12}

kg

answer is A.

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Detailed Solution

The mass of the earth will be

6 \times 10^{24}

kg
Given,
Radius of earth,

r = 6.37 \times 10^{6} m^{}

Acceleration due to gravity,

g = 9.8 m / \sec^{2}

gravitational constant,

G = 6.6 \times 10^{- 11} N m^{2} / {kg}^{2}

We know that,

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

— (1)
Now, put the given value on the equation,

M = \frac{9.8 \times 6.37 \times 6.37 \times 10^{12}}{6.67 \times 10^{- 11}}

\Rightarrow M = \frac{397.65 \times 10^{23}}{6.67}

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

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

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