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JEE Main 2006 (AIEEE) · Torque, Couple & Equilibrium of Rigid Bodies

Torque, Couple & Equilibrium of Rigid Bodies question from JEE Main 2006 (AIEEE)

Q45JEE Main 2006 · AIEEEEasy

Torque, Couple & Equilibrium of Rigid Bodies

A force of −Fk^-F\hat{k} acts on O,O, the origin of the coordinate system. The torque about the point (1,−1)(1,-1) is

Figure

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Answer: (b)

  1. Force acts at O, so r⃗=O−(1,−1,0)=−i^+j^\vec{r} = O - (1,-1,0) = -\hat{i}+\hat{j}.
  2. τ⃗=(−i^+j^)×(−Fk^)=F(i^×k^)−F(j^×k^)=−Fj^−Fi^\vec{\tau} = (-\hat{i}+\hat{j})\times(-F\hat{k}) = F(\hat{i}\times\hat{k}) - F(\hat{j}\times\hat{k}) = -F\hat{j} - F\hat{i}
  3. So the answer is (b) −F(i^+j^)-F(\hat{i}+\hat{j}).
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