Estimate the mass of the moon if the value of acceleration due to gravity on its surface is 1.6 ms^-2 and its radius is 1800 km. Given that G = 6.67 x 10^-11 Nm² kg^-2.

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Solution

Given:
The acceleration due to gravity (g) on the surface of the moon = 1.6 ms^-2.
The radius of the moon (R) = 1800 km = 18,00,000 m = 1.8 x 10⁶ m.
The gravitational constant G = 6.67 x 10^-11 Nm² kg^-2.
Required to find:
The mass of the moon
Solution:
Let the mass of the moon be ‘M’.
The acceleration due to gravity (g) is given by $g = \frac{G M}{R^{2}}$
By substituting the given values, we get
$1.6 = \frac{(6.67 x 10^{- 11}) x M}{{(1.8 x 10^{6})}^{2}} = \frac{(6.67 x 10^{- 11}) x M}{(3.24 x 10^{12})} \Rightarrow 1.6 = 2.05 x 10^{- 23} x M \Rightarrow M = \frac{1.6}{2.05 x 10^{- 23}} = 0.78 x 10^{23} = 7.8 x 10^{22} k g$
Therefore, the mass of the moon is 7.8 x 10²² kg.

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Estimate the mass of the moon if the value of acceleration due to gravity on its surface is 1.6 ms-2 and its radius is 1800 km. Given that G = 6.67 x 10-11 Nm2 kg-2.

Estimate the mass of the moon if the value of acceleration due to gravity on its surface is 1.6 ms^-2 and its radius is 1800 km. Given that G = 6.67 x 10^-11 Nm² kg^-2.