question_answer 43)

                  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 are true ? (The point P is closer to 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 z axis is greater in magnitude than that about z axis.                 (d) Total torque is given be \[\tau =\,\tau +\,\tau '\].                

Answer:

                  (b, c) \[\vec{\tau }=\vec{r}\times \,\vec{F}\] Direction of \[\vec{\tau }\] is perpendicular to the plane containing \[\vec{r}\] and \[\vec{F}\].