Question

The acceleration due to gravity at the surface of the moon is 1.6 m/s². If the radius of the moon is 1.7 x 10^6 m, calculate the mass of the moon.​

Answer 1

Answer:

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Explanation:

$to \: find = \\ mass \: of \: moon \: (M) \\ \\ given = \\ gravitational \: acceleration \: of \: moon \: (g)= 1.6 \: m/s {}^{2} \\ radius \: of \: moon \: (R) = 1.7 \times 10 {}^{6} \: m \\ gravitational \: constant \: (G) = 6.67 \times 10 {}^{ - 11} \: \frac{N.m {}^{2} }{kg {}^{2} } \\ \\ so \: we \: know \: that \\ \\ g = \frac{GM}{ R {}^{2} } \\ \\ 1.6 = \frac{6.67 \times 10 {}^{ - 11} \times \: M }{(1.7 \times 10 {}^{6} ) {}^{2} } \\ \\ M = \frac{1.6 \times (1.7 \times 10 {}^{6}) {}^{2} }{6.67 \times 10 {}^{ - 11} } \\ \\ = \frac{1.6 \times 2.89 \times 10 {}^{12} \times 10 {}^{11} }{6.67} \\ \\ = \frac{4.624 \times 10 {}^{12 + 11} }{6.67} \\ \\ = \frac{4.624 \times 10 {}^{23} }{6.67} \\ \\ = 0.6932533 \times 10 {}^{23} \\ = 6.9325 \times 10 {}^{22} \\ \\ = 6.93 \times 10 {}^{22} \\ ≈7 \times 10 {}^{22} \: \: kg$

$hence \: mass \: of \: moon \: is \\ \: approximately \: \: 7 \times 10 {}^{22} \: \: kg$

Answer 2

Answer:

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