Question

Modulus of elasticity for a perfectly elastic body is
A. Zero
B. Infinity
C. 1
D. Can have any value

Answer 1

Hint: According to various experimental observations and results, the magnitude of the strain produced in a given material is the same irrespective of the fact whether the stress is tensile or compressive. Young’s modulus, denoted by symbol Y is defined as the ratio of the tensile or compressive stress to the longitudinal strain.

Complete step by step answer:
Stress is always proportional to strain for a perfectly elastic body. The graph between stress and strain is always linear. If a body is elastic ideally it means that the infinite linear line from the center of the stress strain graph. This linear line can have a slope making any angle with the x axis. So the values can be anything between 0 and 1. This says that the Young’s modulus can be of any value.
Hence the correct option is D.

Additional Information
The relation between stress and strain can be found experimentally for a given material under tension stress. In a standard test or experiment of tensile properties, a wire or test cylinder is stretched by an external force. The fractional change in length or what is referred to as strain and external force required to cause the strain are noted. The applied external force is gradually increased step by step and the change in length is again noted. Then, the graph plotted between stress and strain gives us an idea about modulus of elasticity.

Note:
It is possible to obtain analogous graphs for compression and shear stress. The stress- strain curves usually vary from one material to another. Such curves help us to know and understand how material deforms with increase in the load.