Question

When a spring is stretched by 2 cm, it stores 100 J of energy. If it is stretched further by 2 cm, the stored energy will be increased by

• A. 100 J
• B. 200 J
• C. 300 J
• D. 400 J

Hint:

Doubling extension quadruples stored energy.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
\(U = \frac{1}{2}kx^2\), so \(U \propto x^2\).
Step 2: Detailed Explanation:
\(100 = \frac{1}{2}k(0.02)^2 \rightarrow k = 5 \times 10^5\ \mathrm{N/m}\)
At \(x = 0.04\) m: \(U = \frac{1}{2}(5 \times 10^5)(0.04)^2 = 400\ \mathrm{J}\)
Increase = \(400 - 100 = 300\ \mathrm{J}\)
Step 3: Final Answer:
Energy increases by 300 J.