The figure shows a lamina in \(\text{XY}\)-plane. Two axes \(\text{z}\) and \(z'\) pass perpendicular to its plane. A force \(\vec{F}\) acts in the plane of the lamina at point P as shown. (The point \(\text{p}\) is closer to the \(z'\)-axis than the \(\text{z}\)-axis.)
(a) | torque \(\vec{\tau}\) caused by \(\vec{F}\) about \(\text{z}\)-axis is along - \(\hat{k}\) |
(b) | torque \(\vec{\tau}'\) caused by \(\vec{F}\) about \(z'\)-axis is along - \(\hat{k}\) |
(c) | torque caused by \(\vec{F}\) about the \(\text{z}\)-axis is greater in magnitude than that about the z'-axis |
(d) | total torque is given by \(\vec{\tau}_{net}=\vec{\tau}+\vec{\tau}'\) |
Choose the correct option:
1. (c, d)
2. (a, c)
3. (b, c)
4. (a, b)
(3) Hint: The direction of the torque depends on the direction of the force and the magnitude f the torque depends on the distance of the force from the axis.
Step 1: Find the direction of the torque about the two axes.
(a) Consider the adjacent diagram, where r > r'.
Torque about z-axis = r x F which is along
(b)
Step 2: Find the magnitude of the torque about the two axes.
(c) the magnitude of the torque about the z-axis where is the perpendicular distance between F and z-axis.
(d) We are always calculating resultant torque about a common axis.
Hence, total torque , because and ' are not about a common axis.
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