Resultants of coplanar non-concurrent forces If a rigid body is acted upon by several coplanar non-concurrent forces, the resulting motion may be which of the following?

Introduction / Context:Understanding how a general system of coplanar non-concurrent forces affects a rigid body is key to predicting motion or ensuring equilibrium in structures and mechanisms.

Given Data / Assumptions:

• Forces lie in a single plane but their lines of action do not meet at one point (non-concurrent).
• Rigid-body assumptions; Newtonian mechanics.

Concept / Approach:A general planar force system can be reduced to a single resultant force and a resultant moment (couple). Depending on whether the net force and/or net moment vanish, the body may translate and rotate (general plane motion), rotate without translation (pure couple), or remain at rest (complete equilibrium).

Step-by-Step Solution:

Verification / Alternative check:Equivalent system reduction (force–couple) always exists in the plane; Chasles’ theorem supports decomposition into translation plus rotation.

Why Other Options Are Wrong:

• Each of A, B, C is possible under specific resultant conditions; hence the combined option “All of these” is correct.
• “Only translation without any rotation” is not guaranteed for non-concurrent systems; a net couple generally exists.

Common Pitfalls:Assuming non-concurrent forces must always cause rotation; if arranged to cancel moments, pure translation can occur, but that requires special geometry.

Final Answer:All of these