Difficulty: Medium
Correct Answer: 80 g
Explanation:
Introduction / Context:
This statics problem couples geometry with equilibrium of a particle acted on by string tensions, weight, and an external horizontal force. Such configurations model pulley/string support systems and help build skill in resolving concurrent forces using geometry-derived direction cosines.
Given Data / Assumptions:
Concept / Approach:
Let the ring be vertically below B at distance y. One segment (B–ring) is vertical; the other (A–ring) is slanted. Use the length constraint to find y and the slanted segment length. Then write horizontal and vertical equilibrium of the ring with two equal tensions T, the horizontal force P, and weight W.
Step-by-Step Solution:
Verification / Alternative check (if short method exists):
Use geometry first to get y = L − AB′ where AB′ is the projected length; the 5–12–13 direction ratios confirm exact arithmetic, giving P = 80 g without rounding errors.
Why Other Options Are Wrong:
40 g and 60 g underestimate the necessary balance of the horizontal component. 100 g overestimates; 120 g equals weight, not the required horizontal balance.
Common Pitfalls (misconceptions, mistakes):
Assuming unequal tensions in a single frictionless string; forgetting that the B–ring segment is vertical and contributes no horizontal component; mixing centimetres and metres inconsistently.
Final Answer:
80 g
Discussion & Comments