Question

Hooke’s law holds good up to
A. Plastic point
B. Limit of proportionality
C. Breaking point
D. None of these

Answer 1

Hint:A spring is said to be in its natural length when no force is applied on the spring. When some force is applied to the spring, it compresses or elongates according to the direction of the applied force. The amount of compression or elongation experienced by the spring is linearly dependent on the applied force within some reasonable tolerance. Hence, we shall not analyze the Hooke’s law.

Complete solution:
The Hooke’s law says that the restoring force experienced by a spring is directly proportional to the extension or compression of a spring. It is expressed as:
${{F}_{restoring}}=-kx$
Where,
${{F}_{restoring}}=$ restoring force acting on the spring
$k=$ spring constant
$x=$ displacement of spring from its natural length

The negative sign here indicates that the restoring force acts in the direction opposite to the displacement of the spring.

Given below is the graph of Hooke’s law experiment. The various points on the graph are as follows:
$A=$ Limit of proportionality
$B=$ Elastic limit or yield point
$E=$ fracture point

It can be seen that only until point A, stress is linear with strain and the material portrays elastic behaviour. Therefore, Hooke’s law holds good only till the limit of proportionality (point A).

Therefore, the correct option is (B) Limit of proportionality.

Note:
After the spring loses its elastic behaviour and starts showing the plastic behaviour, it cannot be restored back to its natural length. The changes made in the orientation of the spring lasts forever. If the force applied on the spring is immense and crosses the fracture point (point E on the graph), then the spring finally breaks.