# Impulse in string

A box of mass $$14~m$$ with smooth base is sliding on an inclined plane of inclination $$\theta=37^{o}$$ under the influence of a force $$F$$. A string of mass $$m$$ length $$l$$ is attached at $$A$$. The box is released from rest and a transverse pulse is produced at other end $$B$$. For $$F=9mg$$ the time taken by the pulse in moving from $$B$$ to $$A$$ will be $$\large{p\sqrt{ \frac{ql}{rg}}}$$. where $$q,r$$ are co prime square free positive integers. find $$p+q+r$$

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