A stable carbon nucleus has 6 protons and 6 neutrons and a radius of 2.7 x 10^{-15} m. The six protons repel each other so that each proton experiences equal resultant force from the others which is also the minimum resultant repulsive force.

For the purpose of calculations, assume that the protons and neutrons are point particles and protons are point charges. Also assume that protons and neutrons get distributed inside or on the surface of sphere of radius given above. The nuclear force which gives nucleus its stability is NOT discussed in this question.

Note: A force F has its component at an angle θ given by F cos θ and in a direction perpendicular to the first (in the same plane), it is F sin θ.

Note: while expressing a number in scientific notation, decimal point should be placed one digit after first non-zero digit and then multiplied by appropriate power of 10, as given in the constants on the front page.

(i) Draw a simple sketch or explain in few words the orientation of the protons in the nucleus when the above mentioned condition is satisfied.

(ii) Obtain the expression for the resultant repulsive force on one proton due to the remaining protons.

(iii) Calculate the magnitude of this resultant repulsive force.

(iv) Calculate the attractive gravitational force on this proton due to the remaining protons under the condition stated above.

(v) Calculate the approximate ratio of the repulsive electrostatic force to the attractive gravitational force.

(vi) What is the direction of the resultant electrostatic repulsive force on this proton?