Question

The gravitational field in a region is given by `vecE=(10Nkg^-1)(veci+vecj)`. Find the work done by an external agent to slowly shift a particle of mass 2 kg from the point (0,0) to a point (5m,4m)`

Answer 1

`vecE=10hati+10hatj`
`vecF=mvecE=20 hati+20hatj`
`W=intvecF.dvecr=int_(x_(1))^(x_(2))F_(x)dx+int_(y_(1))^(y_(2))F_(y)dy`
`=int_(0)^(5)20dx+int_(0)^(4) 20dy`
`=20xx5+20xx4=180 J`
Work done by external agent `=-180 J`
Since particle moves slowly, initial `K.E.=0`
Final `K.E.=0` total work done `=0`
Work done by field `=180 J`
Work done by external agent =`-180 J`