Two springs of spring constants `1500N//m` and `3000N//m` respectively are streched by the same force. The potential energy gained by the two springs will be in the ratio

Explanation

To find the ratio of potential energy gained by two springs with spring constants \( k_1 = 1500 \, \text{N/m} \) and \( k_2 = 3000 \, \text{N/m} \) when stretched by the same force, we can follow these steps:

### Step 1: Understand the relationship between force, spring constant, and extension
The force \( F \) applied to a spring is related to its spring constant \( k \) and the extension \( x \) by Hooke's Law:
\[ F = kx \]
From this, we can express the extension in terms of the force and spring constant:
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