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Q.

The acceleration due to gravity at the moon’s surface is 1.67 ms^-². If the radius of the moon is 1.74 × 10⁶ m. Calculate the mass of the moon. (G = 6.7 × 10^-¹¹ Nm² kg^-²)

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a

7.45×10²¹ kg

b

7.58×10²² kg

c

7.55×10²⁰ kg

d

8.55×10²² kg

answer is A.

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Detailed Solution

$g = \frac{GM}{R^{2}} M = \frac{{gR}^{2}}{G} M = \frac{1.67 \times {(1.74 \times 10^{6})}^{2}}{6.67 \times 10^{- 11}} M = 7.58 \times 10^{22}$

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The acceleration due to gravity at the moon’s surface is 1.67 ms-2. If the radius of the moon is 1.74 × 106 m. Calculate the mass of the moon. (G = 6.7 × 10-11 Nm2 kg-2)