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  • Figure 7.5 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 are true? (The point P is closer to z′-axis than the z-axis.)

Figure 7.5 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 are true? (The point P is closer to the z′-axis than the z-axis.)

(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 \tau caused by F about the z-axis is greater in magnitude than that about the z-axis.

(d) Total torque is given be \tau=\tau +\tau '

Answers (1)

The correct answer is the option (b) and (c)

By right-hand thumb rule, in the formula  \vec{\tau }=\vec{r}\times \vec{F} the direction of \tau is perpendicular to the plane of \vec{r} and  \vec{F}

\overrightarrow{\tau _{z}}=\vec{r}\times \vec{F}=r\; F \sin\; \theta \; \hat{k}

So a is incorrect

\overrightarrow{\tau _{z'}}=\vec{r'}\times \vec{F'}=-r\; F' \sin\; \theta \; \hat{k}

So b is correct

\tau =\tau _{z}+\tau _{z'} is only valid if \tau _{z} and \tau _{z'} are along the same axis, which is not true in this case. Hence d is incorrect.

 

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infoexpert23

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