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The mass of the earth is 6 × 1024 kg. The distance between the earth and the sun is 1.5 × 1011 m. If the gravitational force between the two is 3.5 × 1022 N, what is the mass of the sun? - Science and Technology 1

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Sum

The mass of the earth is 6 × 1024 kg. The distance between the earth and the sun is 1.5 × 1011 m. If the gravitational force between the two is 3.5 × 1022 N, what is the mass of the sun? Use G = 6.7 × 10–11 N m2 kg–2

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Solution

Given: Mass of the earth (Me) = 6 × 1024 kg,

Gravitational force (F) = 3.5 × 1022 N,

Distance (R) = 1.5 × 1011 m,

Gravitational constant (G) = 6.7 × 10-11 Nm2/kg2

The gravitational force between the Sun and the Earth can be found out using the formula,

\[F = \frac{GM_e M_s}{R^2}\]

where, Me and Ms are the masses of the Earth and the Sun, respectively. Using all the given values, we have

\[3 . 5 \times {10}^{22} = (6 . 7 \times {10}^{- 11} )\frac{(6 \times {10}^{24} ) \times M_s}{(1 . 5 \times {10}^{11} )^2}\]

\[ \Rightarrow M_s = \frac{(3 . 5 \times {10}^{22} ) \times (1 . 5 \times {10}^{11} )^2}{(6 . 7 \times {10}^{- 11} ) \times (6 \times {10}^{24} )}\]

`= (7.88 xx 10^44)/(40.2 xx 10^13)`

= 1.96 × 1030 kg

The mass of the Sun is 1.96 × 1030 kg.

Concept: Gravitation
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