A uniform rod of mass `m` and length `l` rests on a smooth horizontal surface. One of the ends of the rod is struck in a horizontal direction at right angles to the rod. As a result the rod obtains velocity `v_(0)`. Find the force with which one-half of the rod will act ont he other in the process of motion.

Explanation

To solve the problem, we need to analyze the motion of the uniform rod after it is struck. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the motion of the rod
When one end of the rod is struck, it begins to move with a linear velocity \( v_0 \) while also rotating about its center of mass. The rod can be considered to be made up of two halves, each with mass \( \frac{m}{2} \).

### Step 2: Determine the relationship between linear and angular velocity
The linear velocity \( v_0 \) at the end of the rod is related to the angular velocity \( \omega \) by the equation:
\[
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