Question:
A body of mass 1 kg starts moving from rest under the action of a force which varies with displacement as $F=2x+5$ (in newtons). The work done by this force to displace the body from $x=0$ to $x=2$ m is:
A body of mass 1 kg starts moving from rest under the action of a force which varies with displacement as $F=2x+5$ (in newtons). The work done by this force to displace the body from $x=0$ to $x=2$ m is:
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For linear force $F=mx+c$, Work is also (Average Force $\times$ Displacement). $F_{avg} = (5 + 9)/2 = 7$; $W = 7 \times 2 = 14$ J.
Updated On: May 5, 2026
- 8 J
- 10 J
- 12 J
- 14 J
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Work done by a variable force is given by $W = \int F dx$.
Step 2: Meaning
Integrate the force function $F=2x+5$ from the limits $x=0$ to $x=2$.
Step 3: Analysis
$W = \int_{0}^{2} (2x+5) dx = [x^2 + 5x]_{0}^{2} = (2^2 + 5(2)) - (0)$.
Step 4: Conclusion
$W = 4 + 10 = 14$ J.
Final Answer: (D)
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