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

Options

A. `12^(@)`
B. `1.2^(@)`
C. `0.12^(@)`
D. `0.012^(@)`

Answer

C

Explanation

Angle of twist at free end
`=30^(@)=(30)/(180)xxpi` rad `=(pip)/(6)` rad
Displacement of the free surface,
`Delta L=(2pi r)/(2 pi)xx(pi)/(6)=(pi r)/(6)=(pixx0.4)/(6)cm`
Angle of shear or shearing strain `=(Delta L)/(L)`
`=(pixx0.4)/(6xx100)` rad. `=(pixx0.4)/(6xx100)xx(180)/(pi)` degree `=0.12^(@)`