Two similar springs `P` and `Q` have spring constant `K_(P)` and `K_(Q)` such that `K_(P) gt K_(Q)`. They are stretched, first by the same amount (case a), then the same force (case b). The work done by the spring `W_(P)` and `W_(Q)` are related as, in case (b), respectively

Options

A. `W_(P) = W_(Q) , W_(P) = W_(Q)`
B. `W_(P) gt W_(Q) , W_(Q) gt W_(P)`
C. `W_(P) lt W_(Q) , W_(Q) lt W_(P)`
D. `W_(P) = W_(Q) , W_(P) gt W_(Q)`

Explanation

To solve the problem, we need to analyze the work done by two springs, P and Q, under two different scenarios: (a) when they are stretched by the same amount and (b) when they are subjected to the same force.

### Step-by-Step Solution:

**Step 1: Understanding the Work Done by Springs in Case A**
- When both springs are stretched by the same amount \( x \), the work done on each spring can be calculated using the formula:
\[
W = \frac{1}{2} k x^2
...