Hint:A Newton spring balance is based on the principle of hooke's law and it contains a spring and a hook on which the weight is balanced. It is used to measure the pulling force by the measure of the displacement of spring, which is attached to the object by the hook.
A Newton spring balance is used to measure the force of the object (weight). We can say that it is a type of weighing machine. When you attach a weight at the end of the spring, there is a force applied to it due to the attached spring and it will extend. As it displaces, you can determine the force due to the attached by looking at the scale or pointer, which shows the extension of the spring. If you attach a heavy weight that is a larger force, then the extension of the spring is more. Thus, the applied force is directly proportional to the extension of the spring.
Thus, the principle used in a Newton spring balance is the extension of the spring is directly proportional to the force pulling it and the option D is correct.
Note:The hooke's law states that the deformation of the spring is directly proportional to the force applied to the spring. The deformation may be positive, which is called extension or negative, which is called compression.
$F \propto x$
Here, the proportionality constant is spring constant.
$F = kx$
Here, $F$ is the force, $x$ is the deformation in spring and $k$ is the spring constant.