How many pieces?

An object is projected with a speed $10\text{ ms}^{-1}$ at an angle of projection, $\theta =\dfrac{\pi}{6}$ with the horizontal. The object breaks down into $n$ fragments of equal mass during its motion. One fragment is found to strike the ground at a distance of $\sqrt{3}\text{ m}$ from the point of projection in the same azimuthal plane, in which the object is projected. If the center of mass of the remaining fragments strike the ground at a distance of $7\sqrt{3}\text{ m}$ from the point of projection, find the value of $n$ .

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