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The acceleration due to gravity on the surface on the moon is $g = 1.67 m / s^{2}$ . If the radius of the moon is $1.74 \times 10^{6} m$ , then find the mass of the moon.

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7.6 \times 10^{20} kg

7.6 \times 10^{22} kg

7.6 \times 10^{10} kg

7.6 \times 10^{16} kg

answer is B.

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Detailed Solution

Given data and assumptions:
The acceleration due to gravity on the moon is

g = 1.67 m / s^{2}

Let the mass of moon be

= M

Radius of the moon,

R = 1.74 \times 10^{6} m

Gravitational constant,

G = 6.67 \times 10^{- 11} N m^{2} / {kg}^{2}

We know, acceleration due to gravity is given by the formula,

g = \frac{G \times M}{R^{2}}

Putting the values of G, M and R in the above equation, we get

\Rightarrow

1.67 = \frac{6.67 \times 10^{- 11} \times M}{{(1.74 \times 10^{6} m)}^{2}}

\Rightarrow

M = \frac{1.67 \times (1.74 \times 10^{6})^{2}}{{6.67 \times 10^{- 11}}^{}}

\Rightarrow

M = 7.6 \times 10^{22} kg

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