KVPY SA Exam 19-Nov-2017 Question Paper

Six objects are placed at the vertices of a regular hexagon. The geometric center of the hexagon is at the origin with objects 1 and 4 on the x-axis (see figure). The mass of the kth object is $\mathrm{mk}=\mathrm{k}\mathrm{M}|\cos {\mathrm{q}}_{\mathrm{k}}|$ where i is an integer, M is a constant with dimension of mass, and ${\mathrm{q}}_{\mathrm{k}}$ is the angular position of the kth verted measured from the positive x-axis in the counter-clockwise sense. If the net gravitational force on a body at the centroid vanishes, the value of i is