Question

Twisting couple per unit angular twist is:
1. \(\dfrac{\pi \eta a^4}{1}\)
2. \(\dfrac{2\pi \eta a^4}{1}\)
3. \(\dfrac{\pi \eta a^4}{21}\)
4. \(\dfrac{\pi \eta a^4}{31}\)

Answer 1

Correct Answer - Option 3 : \(\dfrac{\pi \eta a^4}{21}\)

Concept:

• Twisting couple: It is defined as two equal and opposite forces that act in a different line and contribute to the rotation of the body in a certain direction. 
  • The turning effect, or moment, of a couple, is measured by the product of the magnitude of either force and the perpendicular distance between the action lines of the forces.
  • Twisting a couple per unit twist of a cylinder is also called the torsional rigidity of the modulus.

The formula of Torsional rigidity:

C = \(\dfrac{\pi η a^4}{2l}\)

where,η = coefficient of rigidity, a = radius of the cylinder, l = length.

Explanation:

• From the above discussion, it's clear that the twisting couple per unit angular twist is,

C = \(\dfrac{\pi η a^4}{2l}\)