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A force $\bar{F} = (y^{2} - x^{2} + z^{2}) \hat{i} + (3 xy - 5 z) \hat{j} + 4 z \hat{k}$ is applied on a particle from the point (0,0,0) to the point (2,4,0) in the path shown . If $W_{A}$ is the work done by the force in the paths A, then $W_{A}$ =?

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Correct option is B

The work done by the external force is ∫F→.dS→ . Now here in this case the z coordinate of the motion of the particle is zero. F→=(y2-x2)i^+3xyj^Hence WA=∫02−x2dx+∫043xy dy =[−x33 ]02 +[3y2]04=−83+48=1363

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A force F¯=(y2−x2+z2)i^+(3xy−5z)j^+4zk^ is applied on a particle from the point (0,0,0) to the point (2,4,0) in the path shown . If WA is the work done by the force in the paths A, then WA =?

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A force $\bar{F} = (y^{2} - x^{2} + z^{2}) \hat{i} + (3 xy - 5 z) \hat{j} + 4 z \hat{k}$ is applied on a particle from the point (0,0,0) to the point (2,4,0) in the path shown . If $W_{A}$ is the work done by the force in the paths A, then $W_{A}$ =?