Imagine that the gravitational force between Earth and Moon is provided by an invisible string that exists between the Moon and Earth. What is the tension that exists in this invisible string due to Earth's centripetal force?(Mass of the Moon $= 7.34 \times 10^{22}$ kg, Distance between Moon and Earth $= 3.84 \times 10^{8}$ m)

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Solution

Time period of revolution of moon $T = 27.3 d a y s$
Angular velocity $w = \frac{2 π}{T} = \frac{2 π}{27.3 \times 24 \times 3600} = 2.7 \times 10^{- 6} r a d / s$
Tension on the string $T = M_{m o o n} r w^{2}$
$⟹ T = 7.34 \times 10^{22} \times 3.84 \times 10^{8} \times (2.66 \times 10^{- 6})^{2} = 2 \times 10^{20} N$

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Time period of revolution of moon T=27.3 daysAngular velocity w=2πT=2π27.3×24×3600=2.7×10−6 rad/sTension on the string T=Mmoonrw2⟹ T=7.34×1022×3.84×108×(2.66×10−6)2=2×1020 N