Two rods A and B of the same material and length have radii `r_(1)` and `r_(2)`respective. When they are rigidly fixed at one end and twisted by the same torque applied at the other end, the ratio `[("the angle of twist at the end of A")/("the angle of twist at the end of B")]` equal to

Options

A. `r_(1)^(2)//r_(2)^(2))`
B. `r_(1)^(3)//r_(2)^(3)`
C. `r_(2)^(4)//r_(1)^(4)`
D. `r_(1)^(4)//r_(2)^(4)`

Answer

C

Explanation

Couple needed to twist through an angle `theta` is C
` = [pinr^(4)//2l]theta`n, l and C are constant. `r^(4)theta` = a constant `(theta_(1)//theta_(2)) = (r_(2)^(4)//r_(1)^(4))`