Correct Answer - Option 4 : 420 rpm
Concept:
The power transmitted from pinion = The power gain by gear
Therefore, \({{\rm{T}}_{{\rm{P\;}}}}{{\rm{\omega }}_{\rm{P}}} = {\rm{\;}}{{\rm{T}}_{{\rm{G\;}}}}{{\rm{\omega }}_{\rm{G}}}\)
Calculation:
Given:
No. of teeth on the pinion, ZP = 25, No. of teeth on the gear, ZG = 75, Rotational speed of pinion, NP = 1260 rpm, Rotational speed of gear, NZ = ?
As we know,
\(\frac{{{{\rm{N}}_{\rm{P}}}}}{{{{\rm{N}}_{\rm{G}}}}} = {\rm{\;}}\frac{{{{\rm{Z}}_{\rm{G}}}}}{{{{\rm{Z}}_{\rm{P}}}}}\)
\({{\rm{N}}_{\rm{G}}} = {\rm{\;}}\frac{{{{\rm{Z}}_{\rm{P}}}}}{{{{\rm{Z}}_{\rm{G}}}}}{\rm{\;}} \times {{\rm{N}}_{\rm{P}}}\)
\({{\rm{N}}_{\rm{G}}} = {\rm{\;}}\frac{{25}}{{75}}{\rm{\;}} \times 1260 = 420{\rm{\;rpm}}\)
