A particle is placed in a field characterized by a value of gravitational potential given by `V=-kxy`, where `k` is a constant. If `vec(E)_(g)` is the gravitational field then

Options

A. `vec(E)_(g)=k(xhati+yhatj)` and is conservative in nature
B. `vec(E)_(g)=k(yhati+xhatj)` and is conservative in nature
C. `vec(E)_(g)=k(xhati+yhatj)` and is non-conservative in nature
D. `vec(E)_(g)=k(yhati+xhatj)` and is non-conservative in nature

Answer

B

Explanation

`vec(E)_(g)=(-del/(delx)hati-del/(dely)hatj)(-kxy)`