The force between a hollow sphere $‘S’$ and a point mass $‘P’$ inside it, as shown in figure is :

Statement I : The law of gravitation holds good for any pair of bodies in the universe.

Statement II : The weight of any person becomes zero when the person is at the centre of the earth.

In the light of the above statements, choose the correct answer from the options given below.

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

Four identical particles of mass $\mathrm{M}$ are located at the corners of a square of side $‘a’$ . What should be their speed if each of them revolves under the influence of other’s gravitational field in a circular orbit circumscribing the square?