GATE 2026 AG – Question 56
A tractor PTO shaft drives a grain auger through spur-gear reduction;the auger rotates at 540 rpm. The PTO driving gear has pitch diameter .18 m and transmits 3.5 kW. Tooth normal force along the line of action is 760 N. Assume involute spur gears, single-tooth contact, no friction, and π=3.14. Find pressure angle in degrees, to two decimals.
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Show answer and explanation
Correct answer: 24.00 to 27.00
Explanation
The official calculation treats 540 rpm as the driving-gear speed. Then pitch speed is $v=\pi DN/60=3.14(.18)(540)/60=5.0868$ m/s. Tangential force is $F_t=P/v=3500/5.0868=688.0569$ N. Since $F_t=F_n\cos\phi$, $$\phi=\cos^{-1}(688.0569/760)\approx25.13^\circ.$$ Thus the keyed response is approximately **25.13°**. As printed,540 rpm describes the driven auger and a reduction is mentioned without its ratio;the driver speed is therefore missing. The official result needs the stated implicit speed identification.