A particular of mass ‘m’ moves along the quarter section of the circular path whose centre is at the origin. The radius of the circular path is ‘a’. A force F→$$=yi^$$−$$xj^$$ newton acts on the particle, where x,y denote the coordinates of position of the particle. Calculate the work done by this force in taking the particle from Point A (a$$,$$0) to Point $$B(0$$,$$a)$$ along the circular path.

Question

A particular of mass ‘m’ moves along the quarter section of the circular path whose centre is at the origin. The radius of the circular path is ‘a’. A force F→$$=yi^$$−$$xj^$$ newton acts on the particle, where x,y denote the coordinates of position of the particle. Calculate the work done by this force in taking the particle from Point A (a$$,$$0) to Point $$B(0$$,$$a)$$ along the circular path.

Infinity Learn · Accepted Answer

Work done by force F is $$W=$$∫F→.$$dr=$$∫(yi^$$−$$xj^).(dxi^+dyi^)=$$∫$$(ydx$$−$$xdy)Equation$$ of circular $$pathX2+y2=a2differentiate$$∴$$xdx+ydy=0$$⇒$$dx=-ydyx$$⇒$$W=$$∫$$(y($$−$$ydyx)−$$xdy)=$$−∫$$(x2+y2)xdysubstitute$$, $$X2+y2=a2$$ in above integral $$W=-$$∫$$0aa2a2$$−$$y2dy=$$−π$$a22$$ joule

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