Figure shows force vectors at different points in space for two forces

In figure (a) the force functions is `vec(f)_(1)=f_(0)hat(j)`where `f_(0)` is a constant the force in figure (b) is given by `vec(f)_(2)=f_(0)(x/a)hat(j)` where origin is taken at left corner of the box a is width of the each square box ,mark the correct options.

Options

A. Both forces `vec(f)_(1)` and `vec(f)_(2)` are conservative forces
B. Both forces `vec(f)_(1)` and `vec(f)_(2)` are nonconservative forces
C. `vec(f)_(1)` is conservative `vec(f)_(2)` is non conservative
D. `vec(f)_(1)`is nonconservative vec`(f)_(2)` is conservative

Answer

C

Explanation

Work done in cyclie process for `vec(f)` is zero therefore `vec(f)_(1)` is conservative (all uniform forces are conservative) work done in a cycle proces in case `vec(f)_(2)` is non-zero

` w_(AB) =-F_(AB)l`
`w_(BC)=0`
`w_(CD)=+F_(CD)l`
`W_(BA) =0`
`F_(BA)neF_(CD)`
` :. w_(ABCDA)ne0`