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

A rod of length L and radius r fixed at one end and twisted by applying a torque `tau` at the other end, then the angle of twist `theata` is given by `theta = (2tauL)/(pir^(4)eta)`
Where `eta` is shear modulus of the material of the wire.
As L, `tau and eta` are some for both the wires.
`therefore theta prop (1)/(r^(4)) or(theta_(1))/(theta_(2)) = ((r_(2))/(r_(1)))^(4)`