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 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

The direction of `vectau` is given by right handed screw rule.
According to this rule, the direction of `vectau` caused by `vecF` about z-axis is along `hatk`.
Hence, option (a) is correct.
Again, according to this rule, the direction of `vectau`, caused by `vecF` about `z^(')` axis is along `-hatk`.
Hence, option (b) is also correct.
As `vectau=vecr xx vecF`, and P is closer `z^(')` axis, therefore `vectau` caused by `vecF` about z axis is greater in magnitude than the about `z^(')` axis.
Hence option (c) is also correct.
It is meaningless to add torques about two different axes. Hence option c) is also (d) is incorrect.