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A shaft of diameter 'd' and length L is subjected to twisting moment T, shear angle developed in shaft is 0.001 rad. Now the length of the shaft is doubled, but the diameter and torque remain the same what will be the shear angle?
  • a)
    0.0005 rad
  • b)
    0.001 rad
  • c)
    0.002 rad
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?
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A shaft of diameter d and length L is subjected to twisting moment T, ...



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A shaft of diameter d and length L is subjected to twisting moment T, ...
Given data:
Diameter of shaft (d) = d
Length of shaft (L) = L
Twisting moment (T) = T
Shear angle (θ) = 0.001 rad

We need to find out the new value of shear angle when the length of the shaft is doubled but the diameter and torque remain the same.

Explanation:
The formula to calculate the shear angle in a shaft is:

θ = TL / (GJ)

Where,
T = Twisting moment
L = Length of shaft
G = Modulus of rigidity
J = Polar moment of inertia

We can see that the shear angle is directly proportional to the length of the shaft and twisting moment applied. It is inversely proportional to the polar moment of inertia (which is a function of the shaft diameter) and the modulus of rigidity.

As the diameter and torque remain unchanged, the polar moment of inertia and modulus of rigidity also remain constant. Therefore, the new value of shear angle can be calculated using the formula:

θ' = T(2L) / (GJ)

Where,
θ' = New shear angle
2L = Doubled length of shaft

Substituting the given values in the above formula, we get:

θ' = T(2L) / (GJ) = 2TL / (GJ) = 2(0.001) rad = 0.002 rad

Therefore, the new value of shear angle is 0.002 rad, which is option (c).

Conclusion:
When the length of the shaft is doubled but the diameter and torque remain the same, the new value of shear angle is twice the original value.
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A shaft of diameter d and length L is subjected to twisting moment T, shear angle developed in shaft is 0.001 rad. Now the length of the shaft is doubled, but the diameter and torque remain the same what will be the shear angle?a)0.0005 radb)0.001 radc)0.002 radd)None of theseCorrect answer is option 'B'. Can you explain this answer?
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