Which of the following conditions is INCORRECT for the shafts connected in series to each other?

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SSC JE ME Previous Paper 4 ( Held on: 25 Jan 2018 Morning)
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  1. \(\theta = {\theta _1} + {\theta _2}\)
  2. \(T = {T_1} + {T_2}\)
  3. \({\theta _1} = {\theta _2}\)
  4. Both \(T = {T_1} + {T_2}\;and\;{\theta _1} = {\theta _2}\)

Answer (Detailed Solution Below)

Option 4 : Both \(T = {T_1} + {T_2}\;and\;{\theta _1} = {\theta _2}\)
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Detailed Solution

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Explanation:

Two shafts of different materials can be joined together is two ways:

Shafts in series:

RRB JE ME 41 14Q Full Test 1 Part 1 Hindi - Final Diag(Madhu) images Q1

  • Two shafts are said to be joined in series if the driving torque is applied at one end and the resisting torque at the other end
  • For shafts in series, both the shafts carry the same torque T and the total angle of twist at the resisting end is the sum of separate angles of twist of two shafts
  • T1 = T2
  • \(\theta = {\theta _1} + {\theta _2} = \frac{{T{L_1}}}{{{G_1}{J_1}}} + \frac{{T{L_2}}}{{{G_2}{J_2}}}\)

Shafts in parallel:

RRB JE ME 41 14Q Full Test 1 Part 1 Hindi - Final Diag(Madhu) images Q1a

  • If two or more shafts are rigidly fixed together such that the applied torque is shared between them then the composite shaft so formed is said to be connected in parallel
  • Angle of twist for both the shafts is the same
  • θ1 = θand T = T1 + T2
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