Discussion
Which of the following statements is correct ?
Answer: B
The correct statement is that \(n\) particles with \(k\) holonomic constraints have \(3n - k\) degrees of freedom.
Each free particle in space needs three coordinates, so \(n\) particles need \(3n\). A holonomic constraint is an equation \(f(\mathbf{r}_{1}, \ldots, \mathbf{r}_{n}, t) = 0\) among the coordinates, and each independent one lets us eliminate one coordinate. So \(3n - k\) independent generalised coordinates remain.
A finite system of particles cannot have infinitely many degrees of freedom (that needs a continuum). \(n - k\) forgets the three dimensions of space, and 6 is the number for a single rigid body, not for \(n\) particles in general.
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