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$f = - kx$ , the negative sign in the equation indicates
(A) this force is in same side of the force applied
(B) this force is in opposite side of the force applied
(C) this force is perpendicular side of the force applied
(D) all

Last updated date: 13th Jun 2024
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Hint The force is the vector quantity that it must have both the magnitude and the direction. The value indicates the magnitude of the force and the sign indicates the direction it acts. The positive sign indicates the force is in the direction of the previous force and the negative sign indicates that the force retards or acts against the previous force.
Useful formula:
The Hooke’s law is given by
$f = - kx$
Where $f$ is the restoring force of the spring, $k$ is the spring constant and $x$ is the displacement of the spring when it is stretched.

Complete step by step answer
Let us consider the spring. The spring is considered as the elastic object and when it is stretched and released the object again moves to its original position. This concept was explained by Hooke's law. The restoring force of the spring is the product of the force applied externally and the spring constant.
$f = - kx$
When the spring is pulled, and released the restoring force of the spring causes the spring to move to its original position. Hence the restoring force acts in the opposite to that of the external force applied.

Thus the option (B) is correct.

Note: It is to be remembered that the Hooke’s law is applicable only to the certain limit. That is the stress is directly proportional to the strain only to the certain point. Above that there will be some permanent or the elongation produced. The day today's example of elasticity is the pen with the spring.