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Given that mass of the earth is $6 \times 1 0^{24} kg$ and that of the sun $2 \times 1 0^{30} kg$ . The average distance between the two is $1.5 \times 10 11 m$ . Calculate the force of gravitation between the earth and the sun.

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3.57 \times 1 0^{22} N

7.57 \times 1 0^{22} N

1.57 \times 1 0^{22} N

2.57 \times 1 0^{22} N

answer is A.

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Detailed Solution

The force of gravitation between the earth and the sun is

3.57 \times 1 0^{22}

N

.
We know that the gravitational force of attraction is directly proportional to the product of two
masses and inversely proportional to the square of the distance between them.
This is Newton’s formula.

\Rightarrow F = \frac{G m_{E} m_{S}}{r^{2}}

,
Where

F, G, m_{E}, m_{S},

and

r

represents the force, universal gravitational constant, the mass of the Earth, the mass of the Sun and distance, respectively.
Here,

G = 6.7 \times 1 0^{- 11} N m^{2} k g^{- 2}

m_{E} = 6 \times 1 0^{24} kg

m_{S} = 2 \times 1 0^{30} kg

and

r = 1.5 \times 1 0^{11} m

By putting these values in equation (1),

\Rightarrow F = \frac{(6.7 \times 1 0^{- 11}) (6 \times 1 0^{24}) (2 \times 1 0^{30})}{(1.5 \times 1 0^{11})^{2}}

\Rightarrow F = \frac{6.7 \times 6 \times 2 \times 1 0^{- 11} \times 1 0^{30} \times 1 0^{2}}{2.25}

\Rightarrow F = 35.7 \times 1 0^{21} N .

\Rightarrow F = 3.57 \times 1 0^{22} N .

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