Question

The upper end of a wire of radius $4mm$ and length $100cm$ is clamped and its other end is twisted through an angle of $30$. The angle of shear is:
A. $12$
B. $1.2$
C. $0.12$
D. $0.012$

Answer 1

When shearing stress is applied on the side of an object deformation occurs. This angle of deformation between the sides of the object is called the angle of shear. The twisting angle is the angle through which the fixed end rotates concerning the free end.

Complete step by step solution:
Let us first write the information given in the question.
The radius of the upper end of the wire $r = 4mm = 4 \times {10^{ - 3}}m$, length of the wire $l = 100cm = 1m$
The angle of twist $\theta = {30^o}$.
We have to calculate the angle of shear.
The following is the formula to calculate the angle of shear when the angle of twist is given.
$\phi = \dfrac{{\theta r}}{l}$
Here, $\phi$ is the angle of shear, $\theta$ is the angle of twist, $r$ is the cross-section of the wire, and $l$ is the length of the wire.
Let us now put the values in the above relation.
$\phi = \dfrac{{30 \times 4 \times {{10}^{ - 3}}}}{1}$
Let us further simplify it.
$\phi = {0.12^o}$
Hence, the correct option is (C) ${0.12^o}$.

Note:
Stress is defined as the force that causes the deformation in the object. A rigid body is an idealized condition where we assume that the body cannot be deformed. But generally, objects are rigid to a great extent depending on their physical properties but at some point, they start deforming.
Stress is the force per unit area and its unit is Pascal.
One pascal is defined as a one-newton force acting on $1{m^2}$ an area.