Two wires A and B of same length and of the same material have the respective radii `r_(1)` and `r_(2)`. Their one end is fixed with a rigid support, and at other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be

Options

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

Answer

a

Explanation

As torque, `tau = (pi eta r^(4))/(2l) theta`
In the given problem, `r^(4) theta` = constant
`implies theta prop (1)/(r^(4)) implies (theta_(A))/(theta_(B)) = (r_(2)^(4))/(r_(1)^(4))`