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A \( 5 \mathrm{~kg} \) sphere is connected to a fixed point \( O \) by an inextensible string of length \( 5 \mathrm{~m} \). The sphere is resting on a horizontal surface at a distance \( 4 \mathrm{~m} \) from \( O \). Sphere is given a vertical velocity \( v_{0} \), and it moves freely till it reaches point \( P \), when string becomes taut. Find the maximum allowable velocity \( v_{0}( \) in \( \mathrm{m} / \mathrm{s}) \), if impulse of tension in string is not to exceed \( 6 \mathrm{~N} \) s.
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