A thin unifrom rod of mass `m` and length `l` is free to rotate about its upper end When it is at rest. It receives an impulse `J` as its lowest point, normal to its length immediately after impact.

Options

A. the angular mumentum of the rod is Jl
B. The angular velocity of the rod is `3J//ml`
C. The kinetic energy of the rod is `3J^(2)//2m`
D. Linear velocity of the rod at the mid point is 3J//2m

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the System
We have a thin uniform rod of mass \( m \) and length \( l \) that is free to rotate about its upper end. Initially, the rod is at rest. An impulse \( J \) is applied at the lowest point of the rod, which is normal to its length.

### Step 2: Determine Angular Impulse
The angular impulse \( \Delta L \) imparted to the rod can be expressed as:
\[
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