Color of the Bear Puzzle

The bear is white in color.

We know that:- h = \left( \frac{1}{2} \right )g(t^2) ____________(i)
From here, making g as subject, we get:-
g = \frac{2h}{t^2} ____________(ii)
From the question we know that, h=10 and t= \sqrt2
Substituting them in g, we get:- g = \frac{2\times 10}{(\sqrt2)^2}
Solving the above equation we get :- g=10m/s.
Now we know that only at the poles is the value of g=10m/s.

Therefore this bear was living in the polar region, i.e., it is a polar bear that is white.