Figure shows a lamina in `x-y` plane. Two axes `z` and `z'` pass perpendicular to its plane. A force `F` acts in the plane of lamina at point `P` as shown. Which of the following statements is incorrect ?
(The point `P` is closer to `z'-axis` than the z-axis).
.

Options

A. Torque `tau` caused by F about z- axis is along `-hatk`
B. Torque `tau` caused by F about z'-axis is along `-hatk`
C. Torque `tau` caused by F about z-axis is greater in magnitde to the plane containing r and F.
D. total torque is given be `tau = tau + tau'`

Answer

b,c

Explanation

(A) Consider the adjacent diagram where rgtr
Torque `tau` about z-axis `tau=rxxf` which is along `hatk`

(B) `tau'=r'xxF` which is along `-hatk`
(c ) `|tau|_(z)=Fr_(bot )=` magnitude of torque about z- axis where `r_(bot)` is perpendicular distance between F and z-axis.
SImolarly,`|tau|_(z)'=Fr_(bot)'`
Clearly `r_(bot)gtr_(bot)'implies|tau|_(zgt) |tau|_(z)'`
(d) we are always calculating resltant torque about a common axis .
Hence , total torque `tau ne tau+tau'` because `tau and tau` are not about common axis.