A particle is shifted from `A` to `B` and then from `B` to `C` where `A`,`B` and `C` are the midpoints of the corresponding faces of a cube of side `2m`. If a force `vec(F)=(3hat(i)+4hat(j)-5hat(k))N` is continously acting on the particle, then select incorrect alternative `:-`

Options

A. work done form `A` to `B` is `7J`
B. work done from `B` to `C` is `1J`
C. work done `A` to `C` is `8J`
D. force `vec(F)` is non`-`conservative force .

Answer

D

Explanation

`vec(OA)=hat(i)+hat(k)`, `vec(OB)=2hat(i)+hat(j)+hat(k)`,
`vec(OC)=hat(i)+2hat(j)+hat(k)rArr``vec(AB)=vec(OB)-vec(OA)=hat(i)+hat(j)`
`vec(BC)=vec(OC)-vec(OB)=hat(j)-hat(i)`, `vec(AC)=vec(OC)-vec(OA)=2hat(j)`
`W_(AB)=vec(F).vec(AB)=7`, `W_(BC)=vec(F).vec(BC)=1`
`W_(AC)=vec(F).vec(AC)=8`
A constant force is always a conservative force.