The gravitational force between two objects masses 10\(^{24}\)kg and 10\(^{27}\)kg is 6.67N. Calculate the distance between them [ G = 6.6 x 10\(^{-11}\)Nm\(^2\)kg\(^{-2}\) ]
-
1.0 x 10\(^{20}\)m
- 2.0 x 10\(^{-20}\)m
- 1.0 x 10\(^{-20}\)m
- 2.0 x 10\(^{20}\)m
The correct answer is: A
Explanation
Gravitational force Fg = \(\frac{Gm_1m_2}{r^2}\) = 6.67N
\(m_1\) = 10\(^{24}\)kg, \(m_2\) = 10\(^{27}\)kg, G = 6.6 x 10\(^{-11}\)Nm\(^2\)kg\(^{-2}\) and r = ?
6.67 = \(\frac{ 6.6\times 10^{-11}\times10^{24}\times10^{27}}{r^2}\)
6.67r\(^2\) = 6.6 x 10\(^{40}\)
r\(^2\) = \(\frac{6.6\times10^{40}}{6.67}\) \(\approx\) 9.89 × 10\(^{39}\)
r = \(\sqrt{ 9.89\times10^{39}}\) \(\approxeq\) 9.94 × 10\(^{19}\)m → 1.0 x 10\(^{20}\)m
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