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Question
The ratio of masses of two planets is 2:3 and the ratio of their radii is 4:7 Find the ratio of their accelerations due to gravity.
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Solution
The ratio of masses of two planets m1: m2 = 2 : 3
The ratio of radii of two planets R1: R2 = 4: 7
Formula:
g= `"GM"/R^2` ∴ g ∝ `"M"/"R"^2`
`"g"_1/"g"_2` = `"M"_1/"M"_2` . `"R"_2^2/"R"_1^2` = `2/3xx 7^2/4^2` = `(2xx49)/(3xx16)` = `98/48`
`"g"_1/"g"_2` = `49/24`
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