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.
Explanation:
Specific heat capacity c is defined as heat required to raise temperature of unit mass (1 kg in SI) by 1°C (or 1 K). Formula: Q = mcΔT. Option D describes specific heat in cgs units (cal/g°C), but SI definition uses kg. Options A and C describe latent heats. Memory aid: 'Specific heat = per kg per degree'. This precise definition is crucial for calorimetry problems. Competitive exams often test unit awareness (kg vs g) to distinguish careful students. Always note the mass unit in the definition context.
Explanation:
Work done to charge a capacitor is stored as electrostatic potential energy in the electric field between plates: U = ½QV = ½CV² = Q²/(2C). This energy can be recovered when capacitor discharges. Heat (A) is dissipated in resistance during charging, but ideal capacitor stores energy electrostatically. Memory aid: 'Capacitor energy = ½CV², stored in electric field'. This electrostatics concept is frequently tested in competitive exams. Always distinguish ideal capacitor (no resistance) from real circuits where some energy is lost as heat during charging.
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