Two mating spur gears have 25 teeth and 75 teeth. The pinion rotates at 1260 rpm. What is the rotational speed of gear?

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Two mating spur gears have 25 teeth and 75 teeth. The pinion rotates at 1260 rpm. What is the rotational speed of gear?
1. 1260 rpm
2. 1060 rpm
3. 840 rpm
4. 420 rpm

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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,

$\frac{{{{\rm{N}}_{\rm{P}}}}}{{{{\rm{N}}_{\rm{G}}}}} = {\rm{\;}}\frac{{{{\rm{Z}}_{\rm{G}}}}}{{{{\rm{Z}}_{\rm{P}}}}}$

${{\rm{N}}_{\rm{G}}} = {\rm{\;}}\frac{{{{\rm{Z}}_{\rm{P}}}}}{{{{\rm{Z}}_{\rm{G}}}}}{\rm{\;}} \times {{\rm{N}}_{\rm{P}}}$

${{\rm{N}}_{\rm{G}}} = {\rm{\;}}\frac{{25}}{{75}}{\rm{\;}} \times 1260 = 420{\rm{\;rpm}}$