Question

The equation F=kx describes a force that is

• A. Inversely proportional to displacement
• B. Directly proportional to displacement
• C. Independent of displacement
• D. Equal to displacement

Hint:

Hooke's Law. \(F = kx\). The force exerted by an ideal spring is directly proportional to its displacement from equilibrium.

Answer 1

The Correct Option is B

The equation \(F = kx\) is known as Hooke's Law, which describes the restoring force exerted by an ideal spring.
In this equation: - \(F\) is the force exerted by the spring.
- \(x\) is the displacement from the equilibrium position.
- \(k\) is the spring constant (a measure of stiffness).
The equation states that the force \(F\) is equal to the constant \(k\) multiplied by the displacement \(x\).
This means that the force is directly proportional to the displacement.
If the displacement doubles, the force doubles (assuming k is constant).
The negative sign often included (\(F = -kx\)) indicates that the restoring force is opposite in direction to the displacement, but the magnitude relationship remains directly proportional.