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A mass $m$ connected to inextensible string of length l lie on a horizontal smooth ground. other end of string is fixed. Mass $m$ is imparted a velocity $v$ such that string remains taut motion occurs in horizontal plane. What is impulse provided by string during the time string turns through $90 °$

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$2 m v$

$m v$

$\sqrt{2} m v$

$\sqrt{2 v^{2} - 2 g l}$

answer is C.

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Detailed Solution

Impulse

$= Δ \vec{P} = {\vec{P}}_{f} - {\vec{P}}_{i} = mΔ \vec{v} = m (v \hat{j} - v \hat{i}) | Impulse | = \sqrt{2} mv$

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