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Question: If the mass of earth is 80 times of that of a planet and diameter is double that of planet and ‘g’ o...

If the mass of earth is 80 times of that of a planet and diameter is double that of planet and ‘g’ on earth is 9.8 m/s29.8 \mathrm {~m} / \mathrm { s } ^ { 2 }, then the value of ‘g’ on that planet is

A
B

0.98 m/s20.98 \mathrm {~m} / \mathrm { s } ^ { 2 }

C

0.49 m/s20.49 \mathrm {~m} / \mathrm { s } ^ { 2 }

D

49 m/s249 \mathrm {~m} / \mathrm { s } ^ { 2 }

Answer

0.49 m/s20.49 \mathrm {~m} / \mathrm { s } ^ { 2 }

Explanation

Solution

gp=ge(MpMe)(ReRp)2=9.8(180)(2)2g _ { p } = g _ { e } \left( \frac { M _ { p } } { M _ { e } } \right) \left( \frac { R _ { e } } { R _ { p } } \right) ^ { 2 } = 9.8 \left( \frac { 1 } { 80 } \right) ( 2 ) ^ { 2 }

=9.8/20=0.49 m/s2= 9.8 / 20 = 0.49 \mathrm {~m} / \mathrm { s } ^ { 2 }