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 magnitude than that about z-axis.
D. Total torque is given be `tau = tau + tau'`.

Answer

B, C

Explanation

According to right handed screw rule, the direction of torque `oversetrarr(tau)` caused by `overset rarr(F)` about Z-axis is along `hatk`,
So choice (a) is false.
However choice (b) is true as direction of torque `(overset rarr(tau'))` caused `overset rarr(F)` about Z' axis is along `-hatk`.
As `overset rarr(tau) = overset rarr(r ) xx overset rarr(F)` and `P` is closer to Z' axis, therefore `overset rarr(tau)` caused by `overset rarr(F)` about Z-axis is greater in magnitude than that about Z' axis. Choice (c) is true. Choice (d) is false as it is meanigles to add torques about different axes.