A uniform beam of length 4 m and weight 60 N rests on two supports, one at each end. A 100 N load is placed 1 m from the left support. The reaction at the right support is:
A25 N
B30 N
C75 N
D55 N
Answer & Solution
Correct answer: D. 55 N
1. The beam is in equilibrium under its weight, the load, and the two support reactions.
2. Take moments about the left support to eliminate its reaction from the equation.
3. The 100 N load is at 1 m from the left, so its clockwise moment is 100 × 1 = 100 N·m.
4. The beam's 60 N weight acts at its centre, 2 m from the left, giving 60 × 2 = 120 N·m clockwise.
5. Total clockwise moment about the left support = 100 + 120 = 220 N·m.
6. The right reaction R acts at 4 m from the left, anticlockwise about the left support.
7. R × 4 = 220, so R = 55 N.
8. Hence the right support carries a reaction of 55 N.
_Source: Selina Concise Physics ICSE Class 10, Ch 1 'Force' (icsehelp.com chapter extract)_
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