Choose the correct statements from the following:

1. Hooke’s law is valid up to the limit of proportionality.

2. Hooke’s law is valid up to elastic limit.

3. Limit of proportionality is always less than the elastic limit.

4. Limit of proportionality is either equal to or less than the elastic limit.

The correct answer is

Statement 1: True

Hooke’s Law states that the strain in a solid body is directly proportional to the applied stress and this condition is valid upto the limit of proportionality (i.e. point A in the figure).

\(Stress\; \propto Strain \to \;\sigma \propto \varepsilon \; \to \;\sigma = E\varepsilon \)

Statement 4: True

Limit of proportionality is the stress at which the stress-strain curve ceases to be a straight line. It is the stress at which extension ceases to be proportional to strain. The proportional limit is important because all subsequent theory involving the behavior of elastic bodies is based on the stress-strain proportionality.

Elastic limit is is that point in the stress-strain curve up to which the material remains elastic, i.e. the material regains its shape after the removal of the load.

However, for many materials, elastic limit and proportional limit are almost numerically the same and the terms are sometimes used synonymously. In case where the elastic limit and proportional limit are different, the elastic limit is always greater than the proportional limit.