An object is projected with a speed $10 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle of $30°$ with the horizontal. It breaks into $n$ equal fragments during its motion. One fragment strikes the ground at a distance of $\sqrt{3}\mathrm{ }\mathrm{m}$ from the point of projection. The centre of mass of the remaining fragments strikes the ground at a distance of $7\sqrt{3}\mathrm{ }\mathrm{m}$ from the point of projection. If all fragments strike the ground at the same time, Find the value of $n$ .