The figure shows a lamina in xy-plane. Two axes z and z′ pass perpendicular to its plane. A force →F acts in the plane of the lamina at point P as shown in the figure.
(The point P is closer to the z′-axis than the z-axis.)
| (a) | torque →τcaused by →Fabout z-axis is along (−^k) |
| (b) | torque →τ′caused by →Fabout z′-axis is along (−^k) |
| (c) | torque caused by →Fabout the z-axis is greater in magnitude than that about the z′-axis |
| (d) | total torque is given by →τnet=→τ+→τ′ |
Choose the correct option from the given ones:
| 1. | (c) and (d) only |
| 2. | (a) and (c) only |
| 3. | (b) and (c) only |
| 4. | (a) and (b) only |
Step 1: Find the direction of the torque about the two axes.
Consider the adjacent diagram, where r>r′.
Torque →τ about z-axis =→r×→F which is along ^k
Torque →τ about z′-axis =→r′×→F which is along (−^k)
Step 2: Find the magnitude of the torque about the two axes.
|→τ|z=Fr⊥= the magnitude of the torque about the z-axis where r⊥ is the perpendicular distance between F and z-axis.
Similarly, |→τ|z′=Fr′⊥
Clearly; r⊥>r′⊥⇒|→τ|z>|→τ|z′
We are always calculating resultant torque about a common axis.
Hence, total torque →τnet ≠→τ+→τ′,because →τ and →τ′are not about a common axis.
Hence, option (3) is the correct answer.
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