Rumor had it that Dr. Umerah discovered Planet X. The mass ofthe planet is 4/5 t

Question

Rumor had it that Dr. Umerah discovered Planet X. The mass ofthe planet is 4/5 that of the earth and radius is 2/5 that ofearth. What is the gravity at that planet? ge= gravity ofearth a. 1/5ge b. 16/125ge c. 5ge d. 2ge e. none Can someone so me the steps? Thank You Rumor had it that Dr. Umerah discovered Planet X. The mass ofthe planet is 4/5 that of the earth and radius is 2/5 that ofearth. What is the gravity at that planet? ge= gravity ofearth a. 1/5ge b. 16/125ge c. 5ge d. 2ge e. none Can someone so me the steps? Thank You

Explanation / Answer

Since F=mg and also F=GMm/R2 then we have mg= GMm/R2g= GM/R2 ( on Earth) g'= G (4/5) M/[(2/5) R]2 ( on planet X) The ratio of gravitational acceleration on Earthg to ratio of gravitational accelerationg' on planet X is g/g' = GM/R2 / g'= G (4/5) M/[(2/5) R]2 Now g/g' = 1 / {(4/5) /[(2/5) ]2} g/g' = 1/ (4/5) /[(4/25) ] =(4/25) / (4/5) = 1/5 and finally g/g' = 1/5 or g' =5g or the answer is c. 5ge

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