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Question: Weight of 1 kg becomes 1/6 on moon. If radius of moon is \(1.768 \times 10 ^ { 6 } \mathrm {~m}\), t...

Weight of 1 kg becomes 1/6 on moon. If radius of moon is 1.768×106 m1.768 \times 10 ^ { 6 } \mathrm {~m}, then the mass of moon will be

A

1.99×1030 kg1.99 \times 10 ^ { 30 } \mathrm {~kg}

B

7.56×1022 kg7.56 \times 10 ^ { 22 } \mathrm {~kg}

C

5.98×1024 kg5.98 \times 10 ^ { 24 } \mathrm {~kg}

D

7.65×1022 kg7.65 \times 10 ^ { 22 } \mathrm {~kg}

Answer

7.65×1022 kg7.65 \times 10 ^ { 22 } \mathrm {~kg}

Explanation

Solution

gm=GMmRm2g _ { m } = \frac { G M _ { m } } { R _ { m } ^ { 2 } } and gm=ge6=9.86 m/s2g _ { m } = \frac { g _ { e } } { 6 } = \frac { 9.8 } { 6 } \mathrm {~m} / \mathrm { s } ^ { 2 } =1.63 m/s2= 1.63 \mathrm {~m} / \mathrm { s } ^ { 2 }

Substituting Rm=1.768×106 mR _ { m } = 1.768 \times 10 ^ { 6 } \mathrm {~m} gm=1.63 m/s2g _ { m } = 1.63 \mathrm {~m} / \mathrm { s } ^ { 2 }

and We get Mm=7.65×1022 kgM _ { m } = 7.65 \times 10 ^ { 22 } \mathrm {~kg}