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 `hat k`
B. Torque `tau'` caused by `F` about `z'` axis is along `-hat k`
C. Torque caused by `F` about `z` axis is greater in magnitude than that about `z'` axis.
D. Total torque is given by `tau = tau + tau'`.

Answer

D

Explanation

(d) The direction of `vec tau` is given by right handed screw rule According to this rule, the direction of `vec tau` caused by `vec F` about `z` axis is along `vec k`.
Hence, option (a) is correct.
Again, according to this rule, the direction of `vec tau` caused by `vec F` about `z'` axis is along `- hat k`
Hence, option (b) is also correct.
As `vec tau = vec r xx vec F` and `P` closer `z'` axis. therefore `vec tau` caused about `z'` axis.
Hence ( c) is also correct.
It is meaningless to add torque about twoj different axes.
Hence, option (d) is incorrect.