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Question
The force with which the earth attracts an object is called the weight of the object. Calculate the weight of the moon from the following data : The universal constant of gravitation G = 6.67 × 11−11 N−m2/kg2, mass of the moon = 7.36 × 1022 kg, mass of the earth = 6 × 1024 kg and the distance between the earth and the moon = 3.8 × 105 km.
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Solution
The force between the Earth and the Moon is given by \[F = \frac{GMm}{r^2}\]
Here, M is the mass of the earth; m is the mass of the moon and r is the distance between Earth and Moon.
On substituting the values, we get :
\[F = \frac{6 . 67 \times {10}^{- 11} \times 7 . 36 \times {10}^{22} \times 6 \times {10}^{24}}{3 . 8 \times 3 . 8 \times {10}^{16}}\]
\[= \frac{6 . 67 \times 7 . 36 \times {10}^{35}}{(3 . 8 )^2 \times {10}^{16}}\]
\[ = 20 . 3 \times {10}^{19} = 2 . 03 \times {10}^{20} \]
\[ \approx 2 . 0 \times {10}^{20} N\]
∴ The weight of the moon is \[2 . 0 \times {10}^{20} N\]
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