First slide

Torque

Question

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).

Moderate

A

Torque $τ$ caused by F about Z axis is along $\hat{k}$
B

Torque $τ^{'}$ 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 $τ = τ + τ^{'}$

Solution

The direction of $\vec{τ}$ is given by right handed screw rule.
According to this rule, the direction of $\vec{τ}$ caused by $\vec{F}$ about z axis is along $\hat{k}$ .
Hence, option (1) is correct.
Again, according to this rule, the direction of ${\vec{τ}}^{1}$ caused by $\vec{F}$ about z' axis is along - $\hat{k}$
Hence, option (2) is also correct.
As $\vec{τ} = \vec{r} \times \vec{F}$ and P closer z'axis, therefore, ${\vec{τ}}^{1}$ caused about z' axis is smaller than $\vec{τ}$ .
Hence option (3) is also correct.
It is meaningless to add torques about two different axes.
Hence, option (4) is incorrect.

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