The GATE Grind

GATE 2022 AG – Question 26

Farm Machinery · Machine Design · 1 mark · Numerical answer

An open V-belt joins effective pulley diameters .25 m and .65 m at 1 m centre distance. Find the smaller pulley wrap angle in degrees, to two decimals. Use π=3.14.

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Correct answer: 156.00 to 158.00

Explanation

For an open belt, $\sin\alpha=(D-d)/(2C)=.40/2=.20$. The small-pulley contact angle is $180^\circ-2\alpha$. Converting arcsin(.2) with 180/3.14 gives **156.91°**. The larger pulley instead has 180°+2α.

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