Given : \(\vec{F} = (xy^2)\hat{i} + (x^2 y)\hat{j}\) N. The work done by \(\vec{F}\) when a particle is taken along the semicircular path OAB where the coordinates of B are (4, 0) is :

\(zero\) \(\frac{65}{3}\) J \(\frac{73}{4}\) J \(\frac{75}{2}\) J

\(zero\)

\(W = \int F_x.dx + \int F_y.dy\)   \(= \int xy^2.dx + \int x^2ydy\)   \(= \frac{1}{2} \int d(x^2y^2)\)   \(= [\frac{x^2 y^2}{2}]^{(4, 0)}_{(0, 0)} = 0\)