Question

When a long spring is stretched by \(1\ \text{cm}\), the potential energy stored in the spring is \(U_{1}\). If it is stretched by \(4\ \text{cm}\), the potential energy stored in it is \(U_{2}\). The difference between the energy is

• A. \(9U_{1}\)
• B. \(10U_{1}\)
• C. \(15U_{1}\)
• D. \(16U_{1}\)

Hint:

Spring energy varies as the square of the extension.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The energy stored in a stretched spring is \(U=\dfrac{1}{2}kx^{2}\), so \(U\propto x^{2}\).

Step 2: Calculation
\(\dfrac{U_{2}}{U_{1}}=\left(\dfrac{4}{1}\right)^{2}=16\), so \(U_{2}=16U_{1}\).

Step 3: Difference
\(U_{2}-U_{1}=16U_{1}-U_{1}=15U_{1}\)

Final Answer:
The difference in the stored energy is 15 U1. \[ \boxed{\text{(C) }15U_{1}} \]