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A ball of mass m is moving towards a batsman at a speed v. The batsman strikes the ball and deflects it by an angle $θ$ without changing its speed. The impulse imparted to the ball is

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$mv \cos θ$

$mv \sin θ$

$2 mv \cos (θ / 2)$

$2 mv \sin (θ / 2)$

answer is C.

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Detailed Solution

$After deflection angle between initial and final velocity is θ$

$but they have the same magnitude$

$change in velocity$

$2 v \sin \frac{θ}{2}$

$change in momentum = 2 mvsin (\frac{θ}{2})$

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