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GATE 2021 ME (ME1) – Question 26

Theory of Machines · Balancing of reciprocating and rotating masses · 1 mark · Multiple choice

Consider a reciprocating engine with crank radius R and connecting rod of length L. The secondary unbalance force for this case is equivalent to primary unbalance force due to a virtual crank of

  1. $L^2/(4R)$ at half speed
  2. $R/4$ at half speed
  3. $R^2/(4L)$ at twice speed
  4. $L/2$ at twice speed

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Show answer and explanation

Correct answer: (C) $R^2/(4L)$ at twice speed

Explanation

Secondary inertia force is $m(R^2/L)\omega^2\cos2\theta$. A virtual crank at angular speed 2ω produces $mr_v(2\omega)^2\cos2\theta$.

Equating coefficients yields $r_v=R^2/(4L)$. **Answer: C**, with twice the engine speed.