The force constant of wire is K and its area of cross-section is A. If the force F is applied on it, then the increase in its length will be

The correct option is F/K.

To understand why this is the case, let us break down the relationship between force, the force constant, and the increase in length of a wire under tension.

When a force is applied to a wire, it undergoes deformation (extension). According to Hooke's law, for relatively small deformations within the elastic limit, the extension (increase in length) of an elastic body is directly proportional to the applied force.

This relationship can be mathematically written as:
$F=K·x$
where:
• $F$ is the applied force,
• $K$ is the force constant (representing the stiffness of the wire), and
• $x$ is the increase in the length of the wire.

To find the increase in length ($x$), we can rearrange the formula by isolating $x$:
$x=\frac{F}{K}$

Thus, the increase in the length of the wire is given by the ratio of the applied force to the force constant of the wire, which is written as $F/K$.