A spring of force constant k is stretched by a length x. The work done in stretching it further by the same length x is: MCQ with Answer and Explanation

A spring of force constant k is stretched by a length x. The work done in stretching it further by the same length x is:
A. ³/₂kx²
B. ½kx²
C. kx²
D. 2kx²
Answer: Option A
Solution (By JKExamLibrary)
Work done to stretch spring from 0 to x: W₁ = ½kx². Work done from 0 to 2x: W₂ = ½k(2x)² = 2kx². Thus work for additional stretch from x to 2x: ΔW = W₂ - W₁ = 2kx² - ½kx² = ³/₂kx². Spring force is variable (F=kx), so work is integral of F·dx, yielding parabolic energy storage. Memory aid: Elastic potential energy U = ½kx²; always calculate difference for incremental work. This problem tests understanding of work done by variable forces, a common theme in energy conservation questions in competitive exams.

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This question belongs to: Science Physics
Question #2 Report Error
The specific heat capacity of a substance is defined as the amount of heat required to:
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This question belongs to: Science Physics
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This question belongs to: Science Physics