Question

A spring has a spring constant \( k \). When the spring is stretched through 1 cm, the potential energy is \( U \). What will be the potential energy if it is stretched by 4 cm?

• A. \( 4U \)
• B. \( 8U \)
• C. \( 16U \)
• D. \( 2U \)

Hint:

The potential energy in a spring is proportional to the square of the extension: \( U \propto x^2 \).

Answer 1

The Correct Option is C

Potential energy stored in a stretched spring is given by: \[ U = \frac{1}{2} k x^2 \] If stretching by \( x = 1 \, \text{cm} \) gives energy \( U \), then: \[ U = \frac{1}{2} k (1)^2 \] If stretched by 4 cm, the energy becomes: \[ U' = \frac{1}{2} k (4)^2 = \frac{1}{2} k \cdot 16 = 16 \left( \frac{1}{2} k \cdot 1^2 \right) = 16U \]