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JEE Main 2025 (4 Apr, Shift 1) · Torque, Couple & Equilibrium of Rigid Bodies

Torque, Couple & Equilibrium of Rigid Bodies question from JEE Main 2025 (4 Apr, Shift 1)

Q8JEE Main 2025 · 4 APR · SHIFT 1Easy

Torque, Couple & Equilibrium of Rigid Bodies

Which of the following are correct expression for torque acting on a body?

A. τ⃗=r⃗×L⃗\vec{\tau} = \vec{r} \times \vec{L}

B. τ⃗=ddt(r⃗×p⃗)\vec{\tau} = \frac{d}{dt}(\vec{r} \times \vec{p})

C. τ⃗=r⃗×dp⃗dt\vec{\tau} = \vec{r} \times \frac{d\vec{p}}{dt}

D. τ⃗=Iα⃗\vec{\tau} = I\vec{\alpha}

E. τ⃗=r⃗×F⃗\vec{\tau} = \vec{r} \times \vec{F}

( r⃗=\vec{r} = position vector; p⃗=\vec{p} = linear momentum; L⃗=\vec{L} = angular momentum; α⃗=\vec{\alpha} = angular acceleration; I=I = moment of inertia; F⃗=\vec{F} = force; t=t = time)

Choose the correct answer from the options given below:

Show answer and solution

Answer: (c)

  1. A: r⃗×L⃗\vec{r}\times\vec{L} is not torque (wrong dimensions), so A is wrong.
  2. B: ddt(r⃗×p⃗)=dL⃗dt=τ⃗\frac{d}{dt}(\vec{r}\times\vec{p}) = \frac{d\vec{L}}{dt} = \vec{\tau}, correct.
  3. C: r⃗×dp⃗dt=r⃗×F⃗\vec{r}\times\frac{d\vec{p}}{dt} = \vec{r}\times\vec{F}, correct; E is the definition, correct.
  4. D: τ⃗=Iα⃗\vec{\tau} = I\vec{\alpha} for a fixed axis, correct.
  5. So the answer is (c) B, C, D and E only.
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