Bulk solids handling facts: which statement below is correct regarding angle of repose/slide, storage vessels, and flotation reagents?

Introduction / Context:
Plant layout and solids handling involve standard terminology (hopper, silo) and basic material properties (angles) as well as reagent roles in mineral processing. This question mixes these facts to test precise definitions.

Given Data / Assumptions:

• Angle of repose vs. angle of slide.
• Definitions of hopper and silo in bulk storage.
• Role of pine oil in flotation circuits.

Concept / Approach:
A hopper is indeed a small bin or funnel-shaped vessel with a sloped/discharging bottom that promotes flow into feeders. Silos are typically tall, vertical storage vessels with relatively small footprints. In flotation, pine oil serves as a frother, not a modifying agent (modifiers include activators/depressants like copper sulfate or sodium cyanide). The angle of slide on a surface usually exceeds or equals the angle of repose of a free heap; it is not generally smaller.

Step-by-Step Solution:
Check (b): matches standard definition of a hopper → correct.Check (a): “repose > slide” is generally false; slide angle on a surface is typically greater or comparable.Check (c): silo described as “short and very wide” is incorrect; silos are commonly tall and slender.Check (d): pine oil is a frother, not a modifying agent → incorrect.

Verification / Alternative check:
Equipment glossaries and flotation reagent tables corroborate: hopper (sloping bottom), silo (tall), pine oil (frother).

Why Other Options Are Wrong:
(a) Misstates relationship of angles.(c) Mischaracterizes typical silo geometry and application.(d) Mislabels reagent function; modifiers are activators/depressants, not frothers.

Common Pitfalls:
Memorizing reagent lists without categories; conflating bins, hoppers, and silos based on shape rather than function.

Final Answer:
A hopper is a small bin with a sloping bottom.