Question

Consider a circular shaft of radius 'R' having the maximum shear stress '$f_s$' developed by an applied torque.

Assertion (A) : The shear stress 'q' at a point on the section having coordinate (0, y) is $\frac{f_{s}y}{R}$

Reason(R) : In the shaft, the shear stress 'q' at a point of coordinate (x, y) is $\frac{f_s}{R}\sqrt{x^2+y^2}$

• A. both A and R are true and R is the correct explanation of A
• B. both A and R are true but R is not a correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The correct option is A both A and R are true and R is the correct explanation of A

Torsion formula,

$\frac{G\theta }{L}=\frac{T}{J}=\frac{f}{r}=\frac{f_s}{R}$

$Forpoint(x,y)r=\sqrt{x^2+y^2}$

$\therefore f=\frac{f_s\sqrt{x^2+y^2}}{R}$

Therefore for point (0, y)

$F=\frac{f_{s}y}{R}$