A force `mhat(i) - 3hat(j) + hat(k)` acts on a point and so the point moves from `(20, 3m, 0) to (0, 0, 7)`. If the work done by the force is `-48` unit, what is the value of m ?

Options

A. `5`
B. `3`
C. `2`
D. `1`

Answer

A

Explanation

Force, `vec(F)= m vec(i) - 3hat(j)+hat(k)`
Due to this force, point moves from A(20, 3m, 0) to B(0, 0, 7).
So, the displacement vector `vec(AB)` is given by
`vec(AB)=-20 hat(i)-3m hat(j) + 7 hat(k)`
Work done `= vec(F). vec(AB)`
`=(m hat(i)-3hat(j)+hat(k)).(-20hat(i)-3 m hat(j)+7 hat(k))`
`=(-20 m + 9 m + 7) ` unit
But work done = - 48 unit, as given
`rArr -11 m + 7 = - 48`
`rArr -11 m = - 55`
`rArr m=5`