Equilibrium Of Rigid Bodies
A uniform beam of weight 200 N and length 4 m rests horizontally on two supports placed at its two ends. What is the upward reaction force provided by each end support?
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About This Question
- Subject
- physics
- Chapter
- rotational motion
- Topic
- equilibrium of rigid bodies
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
100 N
As stated in NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion), a rigid body in static equilibrium must satisfy two independent conditions: the net external force on it must be zero, and the net torque about any chosen point must also be zero. The first condition prevents translation, while the second prevents rotation. The uniform beam has its entire weight acting effectively at its centre of mass, which lies at the midpoint and is therefore equidistant from both end supports. Because of this symmetric loading, both supports must share the load equally. The vertical force balance gives R₁ + R₂ = 200 N. Taking torques about either end, with the weight acting at the midpoint a distance 2 m from each support, forces R₁ = R₂. Hence each reaction is R = 200/2 = 100 N. The option 200 N wrongly assigns the entire weight to a single support. The option 50 N halves the correct result a second time without any justification. The option 400 N doubles the total weight, violating the force balance. A check confirms the two upward reactions sum to 200 N, exactly balancing the beam's weight and satisfying both the force and torque equilibrium conditions simultaneously.
This medium difficulty physics question is from the chapter rotational motion, covering the topic of equilibrium of rigid bodies. It appeared in the 2025 exam.
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