Final answer:
The scale reading will be greatest when the elevator descends with decreasing speed, as this causes an upward acceleration increasing the tension in the scale, and least when descending with increasing speed, due to downward acceleration reducing the scale's tension.
Step-by-step explanation:
When considering a weight hanging by a spring scale from the ceiling of an elevator, we need to understand how acceleration affects the force measured by the scale (often perceived as the apparent weight). The reading of the spring scale shows the tension in the spring, which changes with the elevator's motion. Let's examine each scenario:
- (a) Elevator at rest: The scale will read the actual weight of the object, as there is no acceleration.
- (b) Elevator rising with uniform speed: With no acceleration (velocity is constant), the scale will still read the true weight of the object.
- (c) Elevator descending with decreasing speed: Here, the elevator is accelerating upward (decreasing its downward velocity), so the scale reads a force greater than the actual weight.
- (d) Elevator descending with increasing speed: The elevator is accelerating downward (increasing its downward velocity), so the scale reading is less than the actual weight.
Therefore, the scale reading will be greatest in scenario (c), where the elevator is descending with decreasing speed (accelerating upwards). The reading will be the least in scenario (d), where the elevator is descending with increasing speed (accelerating downwards). So, the correct option answer is greatest in (c) and least in (d).