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NEET 1995 (AIPMT) · Torque, Couple & Equilibrium of Rigid Bodies

Torque, Couple & Equilibrium of Rigid Bodies question from NEET 1995 (AIPMT)

Q51NEET 1995 · AIPMTEasy

Torque, Couple & Equilibrium of Rigid Bodies

What is the torque of the force F⃗=2i^−3j^+4k^ N\vec{F} = 2\hat{i}-3\hat{j}+4\hat{k}\text{ N} acting at the point r⃗=3i^+2j^+3k^ m\vec{r} = 3\hat{i}+2\hat{j}+3\hat{k}\text{ m} about origin?

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Answer: (d)

  1. τ⃗=r⃗×F⃗\vec{\tau} = \vec{r}\times\vec{F} with r⃗=(3,2,3)\vec{r} = (3,2,3), F⃗=(2,−3,4)\vec{F} = (2,-3,4).
  2. τx=2(4)−3(−3)=17\tau_x = 2(4)-3(-3) = 17, τy=−[3(4)−3(2)]=−6\tau_y = -[3(4)-3(2)] = -6, τz=3(−3)−2(2)=−13\tau_z = 3(-3)-2(2) = -13
  3. So the answer is (d) 17i^−6j^−13k^17\hat{i}-6\hat{j}-13\hat{k} N m.
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