GATE AG 2022 • Q21 NAT • 1 Mark

Section 2: Farm Machinery

Machine Design

Subtopic: Design and selection of machine elements – gears, pulleys, chains and sprockets and belts

Question Statement:

An open V-belt is wrapped around V-pulleys having effective diameters of 0.25 m and 0.65 m, and their centres are 1 m apart. Assuming ideal conditions, the wrap angle in degree for the smaller pulley is __________. [round off to two decimal places] (Take π = 3.14)

Official Answer Key:

156.00 to 158.00

Step-by-Step Solution & Explanation

• R=0.325m, r=0.125m, C=1m; α=sin⁻¹[(R−r)/C]=sin⁻¹(0.200)=11.537° • Smaller pulley wrap angle = 180° − 2α = 180 − 23.074 = 156.93° Computed value: θ_small ≈ 156.93° (within official range 156.00–158.00)

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