The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle of 30° . Then angle of shear is

The correct option is 0.12°.

When a cylindrical wire of length $L$ and radius $r$ is clamped at one end and twisted through an angle of twist $\theta$ at the free end, the displacement at the surface leads to an angle of shear $\phi$. The relationship between the angle of twist and the angle of shear is given by:
$r\theta =L\phi$
Rearranging the formula to solve for the angle of shear $\phi$ gives:
$\phi =\frac{r\theta }{L}$

Given the following values from the problem:
Radius of the wire, $r=4\text{mm}=0.4\text{cm}$
Length of the wire, $L=100\text{cm}$
Angle of twist, $\theta =30°$

Substitute these values into the formula to calculate the angle of shear:
$\phi =\frac{0.4\text{cm}\times 30°}{100\text{cm}}$
$\phi =\frac{12°}{100}$
$\phi =0.12°$

Thus, the angle of shear is 0.12°.