Question
Download Solution PDFA rod AB rests with the end A on rough ground and the end B against a smooth vertical wall. The rod is uniform and of weight W. If the rod is in equilibrium in the position shown in figure, the normal reaction at B is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The rod is in equilibrium under the action of three forces: weight W acting at center, normal reaction at A (vertical), and horizontal reaction at B from the smooth wall. Friction at A balances the horizontal reaction.
Equilibrium Equations:
- Vertical: \( R_A = W \)
- Horizontal: \( F_A = R_B \)
- Moment about A: \( R_B \times L \times \sin(30^\circ) = W \times \frac{L}{2} \times \cos(30^\circ) \)
Solving:
\( R_B \times \frac{L}{2} = \frac{W L \cos(30^\circ)}{2} \Rightarrow R_B = W \times \cos(30^\circ) = W \times \frac{\sqrt{3}}{2} \)
Final Answer:
\( \frac{\sqrt{3}}{2} W \)
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