Planet X is very large, having a mass and radius that are, respectively, 338 and

Question

Planet X is very large, having a mass and radius that are, respectively, 338 and 13.8 times that of earth. Suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. Each object falls the same distance before striking the ground. Determine the ratio of the time of fall on planet × to that on earth.

This needs to be solved algebraically. I missed this homework question so if someone could walk me through the steps so I can see where I messed up, I would appreciate it...

Explanation / Answer

g2= GM/r*r

hence the acc due to gravity on this planet shall be 338/(13.8)^2 times the accelaration on earth
i.e g2= 1.775g

ratio of time
as
2S=a(t)^2
hence the ratio of the time shall be square root of the ratio of accelarations

i.e T2/T1=1.775= 1.332

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