Question

Two springs of spring constants \(K\) and \(2K\) are stretched by the same force. If \(W_1\) and \(W_2\) are the energies stored in them respectively, then

• A. \( W_1 = 2W_2 \)
• B. \( W_1 = \frac{W_2}{4} \)
• C. \( W_2 = 2W_1 \)
• D. \( W_1 = W_2 \)

Hint:

For same applied force, energy stored in a spring is inversely proportional to its spring constant.

Answer 1

The Correct Option is A

Step 1: Write expression for energy stored in spring.
\[ W = \frac{F^2}{2k} \]

Step 2: Apply formula to both springs.
\[ W_1 = \frac{F^2}{2K}, \quad W_2 = \frac{F^2}{2(2K)} = \frac{F^2}{4K} \]

Step 3: Find ratio.
\[ \frac{W_1}{W_2} = 2 \Rightarrow W_1 = 2W_2 \]