Question

A body moves from point A to B under the action of a force, varying in magnitude as shown in the figure. Force is expressed in newton and displacement in meter. What is the total work done? }

• A. 37.5 J
• B. 100 J
• C. 12.5 J
• D. 22.5 J

Hint:

Area above the displacement axis is positive work; area below is negative work.

Answer 1

The Correct Option is D

Step 1: Concept
Work done is the area under the Force-Displacement ($F-s$) graph.
Step 2: Analysis
Area from $s=1$ to $s=2$ (Rectangle AP): $1 \times 10 = 10$ J. Area from $s=2$ to $s=3$ (Trapezium PQ): $1/2 \times (10+15) \times 1 = 12.5$ J. Area from $s=3$ to $s=4$ (Triangle QR): $1/2 \times 1 \times 15 = 7.5$ J. Area from $s=4$ to $s=5$ (Triangle RB - below axis): $1/2 \times 1 \times (-15) = -7.5$ J.
Step 3: Calculation
Total Work = $10 + 12.5 + 7.5 - 7.5 = 22.5$ J.
Step 4: Conclusion
Hence, the total work done is 22.5 J.
Final Answer:(D)