Question

Derive the expression for torque per unit Twist of a wire

Answer 1

Expression for Torque per unit twist of a body (C) = $\frac{\pi nr^{4}}{2l} }$, where n is coefficient of rigidity, r is the radius of cylinder and l is the length of the cylinder.

The torque per unit twist of a wire is the twisting couple per unit twist of a cylinder, also known as Torsional Rigidity of the modulus of torsion of the cylinder.

• It is also known as the torsion required to deform a cylinder for a unit rotation for a unit length of a cylinder.
• Torsional Rigidity (C) is similar to the Shear Modulus of a body.

Derivation of the expression -

 Torsional Rigidity is the ratio of shear stress to the angle of deformation.

C = $\frac{\pi nr^{4}}{2l} }$.