Allied & ICAR Exam Bank • ALLIED_0818 MCQ • 1 Mark

Section 2: Farm Machinery

Machine Design

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

Question Statement:

The pitch diameter $D$ of a chain sprocket having $z$ teeth and chain pitch $p$ is given by:

Options:

  • (A) $D = \frac{p}{\sin(180^\circ / z)}$
  • (B) $D = \frac{p}{\cos(180^\circ / z)}$
  • (C) $D = \frac{p \cdot z}{\pi}$
  • (D) $D = p \cdot z$

Answer Key:

A

Step-by-Step Solution & Explanation

From sprocket pitch polygon geometry, $\sin(180^\circ / z) = \frac{p / 2}{D / 2} = \frac{p}{D} \implies D = \frac{p}{\sin(180^\circ / z)}$.
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