Two springs A and B `(K_A = 2 K_B)` are stretched by same suspended weights then ratio of workdone in stretching is -

Options

A. `1:2`
B. `2:1`
C. `1:1`
D. `1:4`

Explanation

To solve the problem of finding the ratio of work done in stretching two springs A and B, where the spring constant of spring A is twice that of spring B (i.e., \( K_A = 2 K_B \)), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Work Done on a Spring**:
The work done \( W \) in stretching a spring is given by the formula:
\[ W = \frac{1}{2} k x^2 \]
where \( k \) is the spring constant and \( x \) is the extension of the spring.

2. **Identify the Spring Constants**:
Let:
- \( K_A = 2 K_B \)
- Let \( K_B = k \), then \( K_A = 2k \).

3. **Assume the Same Extension**:
Since both springs are stretched by the same weight, we assume they are stretched by the same distance \( x \).

4. **Calculate Work Done on Each Spring**:
- For spring A:
\[ W_A = \frac{1}{2} K_A x^2 = \frac{1}{2} (2k) x^2 = k x^2 \]
- For spring B:
\[ W_B = \frac{1}{2} K_B x^2 = \frac{1}{2} k x^2 \]

5. **Find the Ratio of Work Done**:
Now, we can find the ratio of work done in stretching spring A to work done in stretching spring B:
\[ \frac{W_A}{W_B} = \frac{k x^2}{\frac{1}{2} k x^2} = \frac{k x^2}{\frac{1}{2} k x^2} = \frac{1}{\frac{1}{2}} = 2 \]

6. **Final Ratio**:
Therefore, the ratio of work done in stretching spring A to work done in stretching spring B is:
\[ W_A : W_B = 2 : 1 \]

### Conclusion:
The final answer is that the ratio of work done in stretching spring A to work done in stretching spring B is \( 2 : 1 \).