GATE ME 2024 Set 1 — Question 27
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Engineering Mechanics → Statics → Free-Body Diagrams & Equilibrium
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Question
A rigid massless tetrahedron is placed such that vertex O is at the origin and the other three vertices A, B, and C lie on the coordinate axes as shown in the figure. The body is acted on by three point loads, of which one is acting at A along -axis and another at point B along -axis. For the body to be in equilibrium, the third point load acting at point O must be
Correct answer
(B) in x - y plane but not along x or y axis
Solution
For the rigid body to be in equilibrium, both the net force and the net moment must be zero.
1.Moment Equilibrium: Let the force at A be and the force at B be . The position vectors are and .
Taking moments about the origin O:Thus, moment equilibrium about O is already satisfied.2.Force Equilibrium: Let the third force acting at O be .
This resultant force lies in the plane. Since it has both and components (assuming ), it is not aligned with either the or axis. Therefore, the third load must be in the plane but not along the or axis.Correct option is (B).Continue learning with Success Tracker
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