A 2 m cantilever carries point loads of 300 N, 500 N and 800 N at 0.5 m, 1.2 m and 2 m from the fixed end. The shear force (N) at the fixed end and bending moment (N·m) at the free end are:
Try it first: pick an option, then read the explanation.
Correct answer: C. 1600, 0
Asked in SSC JE 14/11/2022
Detailed Explanation
The shear at the fixed end of a cantilever is the total load on it. The bending moment at the free end is always zero unless a couple is applied there — a load at the free end has no lever arm about that point.
\[ V_A = 300 + 500 + 800 = 1600\ \text{N} \]
\[ M_D = 800 \times 0 = 0 \]
Why “1600, 0” Is Correct
The pair is 1600 N and 0 — option (c). (For comparison, the fixed-end moment would be 2350 N·m.)
Why the Other Options Are Wrong
- A. 800, 640: 800 N is the shear near the free end; 640 N·m is the moment at C.
- B. 500, 2350: 2350 N·m is the moment at the fixed end, not the free end.
- D. 800, 0: 800 N is the shear in the last segment only, not at the fixed end.
Key Point
Cantilever: V at fixed end = total load; M at free end = 0 (no end couple).
Key Concepts for Students
- Bending moment is maximum at the fixed end for downward loads.
- The shear in each segment = sum of the loads beyond it.
- A free end has zero BM, and zero SF unless a load acts exactly there.
Practice more: this is question 18 in Bending Moment and Shear Force MCQs – Part 2. Try the whole set and check every answer instantly.