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Supposing we have a uniformly mass distributed hemisphere of some radius, so what will be direction of gravitational field throughout the flat surface of hemisphere? And why?

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In the flat, you will feel it falls down the mountain side to the center Due the direction of gravity would be at the center of mass.

A picture is worth a thousand words.

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In a uniformly mass distributed hemisphere of radius r, the center of mass is given by geometric centroid. The geometric centroid of an heisphere is then given by 3/8 * r

http://mathworld.wolfram.com/Hemisphere.html

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    $\begingroup$ You're assuming that the direction of the gravitational acceleration always points towards the centre of mass, and in general this is not true. $\endgroup$ Commented Nov 14, 2014 at 17:36

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