Correct Answer - Option 3 : 628.3 mm/s
Concept:
Rolling velocity/Pitch line velocity:
Rolling velocity = Pitch line velocity = ω × r
where ω = angular velocity (rad/sec) and r = pitch circle radius.
Module:
\(m=\frac{D}{T}\;ot\;D=mT\)
\(r=\frac{mT}{2}\)
where T = number of teeth and m = module.
Calculation:
Given:
T = 30, m = 2 mm, N = 200 rpm
Pitch line velocity:
V = ωr
\(V =\frac{2\pi N}{60}\times\frac{mT}{2}\)
\(V =\frac{2\pi\;\times\;200}{60}\times\frac{2\;\times\;30}{2}=628.3\;mm/s\)