The work done by the force `vec(F)=A(y^(2) hati+2x^(2)hatj)`, where A is a constant and x & y are in meters around the path shown is :

Options

A. zero
B. Ad
C. `Ad^(2)`
D. `Ad^(3)`

Answer

D

Explanation

`W=intvec(F).vec(dx)=intA(y^(2)hati+2x^(2)hatj).(dx hati+dy.hatj)`
`=Aint(y^(2)dx+2x^(2)dy)`
`W_(OA)=0+0,W_(AB)-A[0+2d^(2)d]`
`W_(BC)=A[d^(2)(-d)+0],W_(CD)=A[0+0]`
`W=0+2ad^(2)-Ad^(3)+0=Ad^(3)`