Question

Mass of a planet is twice that of the earth and its radius is four times of the earth.find the value of g on its surface

Answer 1

That would be 5/9 times the acceleration due to gravity of earth. Approximately 5.45 m/s^2.

If you would like to know how I arrived at this result, comment, and I will edit this answer. Cheers :)

UPDATE - To avoid confusion, I'm gonna tell you how I calculated the acceleration due to gravity without any tough calculations - 

The earth's acceleration due to gravity is 9.8 m/s^2 (approx). The formula of acceleration due to gravity is given by this formula - 

g=GMr2g=GMr2
whre G is the Gravitation Constant, M is the mass of the body and r is it's radius.

From the above equation, it is clear that the acceleration due to gravity is directly proportional to the mass and inversely proportional to the square of the radius of the object. This means that if you increase the mass of the body by 5 times, the acceleration due to gravity would also increase by 5 times. And if you increase the radius by 3 times, the acceleration due to gravity would decrease by 9 times (because it's inversely proportional to the square of the radius). Thus, if you increase the mass by 5 times and at the same time increase the radius by 3 times, the new acceleration due to gravity would be 5959 times the previous value.

So, if a planet has a mass 5 times greater than earth and radius 3 times greater than earth, it's acceleration due to gravity would be 5959 times than that of earth. 

Multiplying 5/9 by 9.8, we get g=5.45 m/s^2.

No big numbers involved, gravitation constant's value not involved.
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Cheers :)

Answer 2

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