The torsional resistance of a shaft is directly proportional to

 Pick up the incorrect statement from the following: The torsional resistance of a shaft is directly proportional to

A) modulus of rigidity

B) angle of twist

C) reciprocal of the length of the shaft

D) moment of inertia of the shaft section

Solution-

Using torsion equation ,

TJ=GθL=τR$\frac{\mathrm{T}}{\mathrm{J}}=\frac{\mathrm{G}\theta }{\mathrm{L}}=\frac{\tau }{\mathrm{R}}$

$\frac{\mathrm{<br>}}{}$

Where,

T = torsion applied, J = Polar moment of inertia, G = modulus of rigidity,

θ = Twist of cross-section, L = Length of the shaft,

τ = Maximum shear stress due to torsion and R = Radial distance from the centre of the shaft

From the above equation, torsional resistance of a shaft is directly proportional to the modulus of rigidity, angle of twist, maximum shear stress due to torsion, polar moment of inertia while inversely proportional to the length of the shaft and radial distance from the centre of the shaft.

Thus, it does not depends on the moment of inertia of the shaft section but depends on the polar moment of inertia of the shaft.

∴ The torsional resistance of a shaft is directly proportional to the modulus of rigidity, angle of twist, reciprocal of the length of the shaft.