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

1. Torque τ caused by F about z axis is along `-hatk`.
2. Torque τ′ caused by F about z′ axis is along `-hatk`.
3. Torque τ caused by F about z axis is greater in magnitude than that about z axis.
4. Total torque is given be τ = τ + τ′.

Answer 1

b and c

Explanation:

a. Consider the adjacent diagram where r > r'

Torque τ about z-axis τ = r × F which is along `hatk`

b. τ' = r' × F which is along `- hatk`

c. |τ|_z = Fr_⊥ = magnitude of the torque about z-axis where r_⊥ is the perpendicular distance between F and z-axis.

Similarly, |τ|_z = Fr_⊥'

Clearly r_⊥ > r_⊥

⇒ |τ|_z > |τ|_z

d. We are always calculating resultant torque about a common axis. Hence, total torque τ ≠ τ + τ', because τ and τ' are not about the common axis.