• # question_answer The work done by the force $\vec{F}=A\,({{y}^{2}}\hat{i}+2{{x}^{2}}\hat{j}),$ where A is a constant and x & y are in meters around the path shown is: A) zero       B) A d C) $A\,{{d}^{2}}$ D) $A\,{{d}^{3}}$

 $W=\int{\vec{F}\cdot d\bar{x}}=\int{A\,({{y}^{2}}\,}\hat{i}+2{{x}^{2}}\hat{j})\cdot (dx\,\hat{i}+dy\cdot \hat{j})$ $=A\int{({{y}^{2}}\,dx+}2{{x}^{2}}dy)$ ${{W}_{OA}}=0+0,$${{W}_{AB}}=A\,[0+2{{d}^{2}}\,d]$ ${{W}_{BC}}=A\,[{{d}^{2}}\,(-\,d)+0],$${{W}_{CD}}=A\,[0+0]$ $W=0+2A{{d}^{3}}-A{{d}^{3}}+0=A{{d}^{3}}$