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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

हिन्दी

Which of the following conditions is both necessary and sufficient for the centre of mass of a continuous body to coincide with its geometric centre?

  1. The body must be homogeneous and possess reflection symmetry about planes passing through its geometric centre.
  2. The body must be in pure rotational equilibrium under external forces.
  3. The body must be planar with uniform thickness only.
  4. The total external torque acting on the body must be zero.

Correct answer · Option 1

The body must be homogeneous and possess reflection symmetry about planes passing through its geometric centre.

Explanation

Due to uniform density and reflection symmetry, every element \( dm \) at \( (x,y,z) \) cancels with \( dm \) at \( (-x,-y,-z) \), making \( \int \mathbf{r} dm = 0 \) at the geometric centre.

Related questions

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