# 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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