A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force  F→=αyi^+2αxj^N, where x and y are in meter and  α=−1Nm−1. The work done on the particle by this force F→ will be ___ Joule.

For AB:y= const F→=−yi^−2xj^⇒F→=−i^−2xj^dr→=dxi^ So, WAB=∫x=01 F→⋅dr→=∫01 −dx=−1J For BC:x=constF→=−yi^−2j^dr→=dyjWBC=∫y=10.5 −2dy⇒WBC=+1J For CD:y=const F→=−0.5i^−2xj and dr→=dxi^WCD=∫10.5 −0.5dx=0.25J For DE:x= const F→=−yi^−j^dr→=dyj^WDE=∫y=0.50 −dy=+0.5J For EF:y=0 F→=−2×j^dr→=dxi^⇒WEF=0 For FA:x=0 F→=−yi^dr→=dyj^⇒WFA=0WNet=−1+1+0.25+0.5=0.75J