Six forces lying in a plane and forming angles of 60⁰ relative to one another are applied to the center of a homogenous sphere with a mass $\mathrm{m}=6$ kg. These forces are radially outward and consecutively 1N, 2N, 3N, 4N, 5N and 6N. The acceleration of the sphere is 

The particle is acted upon by 6 forces radially outwards. Net force along each diameter is 3N. Thus, three forces of 3N with an angle of 60 degrees between them are acting on the sphere.
Then resultant will have three force each of 3N at 60 degrees between them.

Then resultant two 3 N forces at 120 degrees will be 3 N along 3rd 3 N force.

Now, the resultant of the final forces will be $3N+3N=6\mathrm{N}$.

So, the acceleration will be a = 6/6 = 1ms^-2.