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In an \( X Y \) horizontal plane a force field \( \vec{F}=-(40 \mathrm{~N} / \mathrm{m}) \) \( (y \hat{i}+x \hat{j}) \) is present where \( x \) and \( y \) are the coordinates of any point on the plane. A smooth \( \operatorname{rod} A B \) is fixed in the plane as shown in the figure. A particle of mass \( 5 \mathrm{~kg} \) is to be released with a velocity in this force field such that it reaches to point \( B \). Find the minimum velocity that must be imparted along the rod at \( A \) such that it reaches to \( B \).
Figure \( 3.73 \)
(A) \( 1 \mathrm{~m} / \mathrm{s} \)
(B) \( 2 \mathrm{~m} / \mathrm{s} \)
(C) \( 3 \mathrm{~m} / \mathrm{s} \)
(D) \( 4 \mathrm{~m} / \mathrm{s} \)
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