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JEE Main 2021 (16 Mar, Shift 2) · Torque, Couple & Equilibrium of Rigid Bodies

Torque, Couple & Equilibrium of Rigid Bodies question from JEE Main 2021 (16 Mar, Shift 2)

Q23JEE Main 2021 · 16 MAR · SHIFT 2Medium

Torque, Couple & Equilibrium of Rigid Bodies

A force F⃗=4i^+3j^+4k^\vec{F} = 4\hat{i} + 3\hat{j} + 4\hat{k} is applied on an intersection point of x = 2 plane and x-axis. The magnitude of torque of this force about a point (2, 3, 4) is ___________. (Round off to the Nearest Integer)

Numerical answer type. Work it out, then open the answer.

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Answer: 20

  1. Point of application: x=2x = 2 plane meets x-axis at (2,0,0)(2,0,0).
  2. r⃗=(2,0,0)−(2,3,4)=(0,−3,−4)\vec{r} = (2,0,0)-(2,3,4) = (0,-3,-4), F⃗=(4,3,4)\vec{F} = (4,3,4)
  3. τx=(−3)(4)−(−4)(3)=0\tau_x = (-3)(4)-(-4)(3) = 0, τy=−[0(4)−(−4)(4)]=−16\tau_y = -[0(4)-(-4)(4)] = -16, τz=0(3)−(−3)(4)=12\tau_z = 0(3)-(-3)(4) = 12
  4. ∣τ⃗∣=162+122=20|\vec{\tau}| = \sqrt{16^2+12^2} = 20
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