Two blocks each of mass m are joined together using an ideal spring of force constant K and natural length `l_(0)` . The blocks are touching each other when the system is released from rest on a rough horizontal surface. Both the blocks come to rest simultaneously when the extension in the spring is `(l_(0))/4`. The coefficient of friction between each block and the surface (assuming it to be same between any of the blocks and the surface) is :

Options

A. `(Kl_(0))/(40 mg)`
B. `(Kl_(0))/(8 mg)`
C. `(3 Kl_(0))/( 8 mg)`
D. `17/20 (Kl_(0))/(mg)`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the System
We have two blocks, each of mass \( m \), connected by an ideal spring with force constant \( K \) and natural length \( l_0 \). The blocks are initially touching each other and are released from rest on a rough horizontal surface. The extension in the spring when the blocks come to rest is \( \frac{l_0}{4} \).

### Step 2: Determine the Total Extension
The total extension in the spring when the blocks come to rest is given as \( \frac{l_0}{4} \). Therefore, the final length of the spring is:
\[
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