A block of mass m moving with a velocity `v_(0)` on a smooth horizontal floor collides with a light spring of stiffness k that is rigidly fixed horizontally with a vertical wall. If the maximum force imparted by the spring on the block is F, then:
(A) `F prop sqrt(m) " " (B) F prop sqrt(k)`
(C) `F prop v_(0) " " ` (D) None of these

Explanation

To solve the problem, we need to analyze the situation where a block of mass \( m \) collides with a spring of stiffness \( k \). The block is initially moving with a velocity \( v_0 \) on a smooth horizontal floor. When the block compresses the spring, it will eventually come to rest at maximum compression before the spring pushes it back.

### Step-by-Step Solution:

1. **Identify Initial and Final Energies:**
- The initial kinetic energy (\( E_i \)) of the block can be expressed as:
\[
E_i = \frac{1}{2} m v_0^2
...