Calculate the minimum diameter of the shaft, such that the shearing stress does NOT exceed 50 N/mm2 during torque transmission of 15000 N-m.

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SSC JE Mechanical 07 Jun 2024 Shift 2 Official Paper - 1
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  1. 98.4 mm
  2. 120.6 mm
  3. 100.2 mm
  4. 115.2 mm

Answer (Detailed Solution Below)

Option 4 : 115.2 mm
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Detailed Solution

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Concept:

We use the torsion formula for solid circular shafts to determine the minimum diameter required to ensure the shear stress does not exceed a specified limit during torque transmission.

Given:

  • Maximum allowable shear stress,
  • Torque transmitted,

Step 1: Recall the torsion formula

The shear stress in a solid shaft is given by:

where is the diameter of the shaft.

Step 2: Rearrange the formula to solve for diameter

Step 3: Substitute the given values

Step 4: Calculate the diameter

 

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