Question

The ratio of the change in dimension at right angles to the applied force to the initial dimension is known as
A. ${\text{Y}}$
B. $\eta$
C. $\beta$
D. ${\text{K}}$

Answer 1

When we apply force to stretch or to compress a particular material there will be change in length of that material. That change can happen along the direction of applied force or perpendicular to the direction of applied force or length might change in three dimensions due to that application of force.

Complete answer:
When a force is applied on the given cross section area then it will produce the stress which is given by the ratio of force applied to the cross-section area. Due to the application of force the ratio of change in length to the original length is called strain. The ratio of stress and strain is called a young's modulus which is denoted by ${\text{Y}}$.
Now when we apply force in one direction then length will change along that direction and will also change along perpendicular direction. So strain will be created in both directions. The perpendicular strain is called lateral strain and the parallel strain to the direction of application of force is called longitudinal strain. The ratio of lateral to the longitudinal strain is called the poisson's ratio and denoted by $\eta$.
Shearing strain is nothing but when we apply force tangent to the surface the angle between the lines which are initially perpendicular changes, that change in angle is called shearing strain and denoted by
${\text{K}}$
The perpendicular strain which is generated when we apply force perpendicular to any surface is called lateral strain and denoted by $\beta$.

So, the correct answer is “Option C”.

Note:
One might confuse this with poisson’s ratio, poisson’s ratio is ratio of strains while lateral strain is the ratio of lengths. While both the poisson’s ratio and lateral strain are dimensionless. While considering poisson’s ratio we will consider only the magnitude of the ratio of strains because lateral strain generally will be negative when longitudinal strain is positive.