Question: 19: The restoring force of a spring with a block attached to the free end of the spring is represented by:
Answer: Option (4)
Explanation:
The restoring force exerted by a spring follows Hooke’s law.
According to Hooke’s law, the restoring force is directly proportional to the displacement of the block from its mean position and acts in the opposite direction.
Mathematically, it is given by
F_x = -kxwhere k is the spring constant and x is the displacement.
This equation represents a straight-line relationship between force and displacement.
The negative sign indicates that the force is opposite in direction to the displacement.
Hence, the graph of F_x versus x is a straight line passing through the origin with a negative slope.
Among the given options, only option (4) shows a straight line through the origin with negative slope, correctly representing the restoring force of a spring.
Therefore, the correct option is (4).