A uniform rod of length `l` and mass 2 m rests on a smooth horizontal table. A point mass `m` moving horizontally at right angles to the rod with velocity `v` collides with one end of the rod and sticks it. Then

Options

A. angular velocity of the system after collision is `(2)/(5)(v)/(l)`
B. angular velocity of the system after collision is `(v)/(2l)`
C. The loss in kinetic energy of the system as a whole as a result of the collision `(3)/(10)mv^(2)`
D. The loss in kinetic energy of the system as a whole as a result of the collision `(7mv^(2))/(24)`

Explanation

To solve the problem step by step, we will analyze the collision of the point mass with the rod and calculate the angular velocity and the loss in kinetic energy.

### Step 1: Understand the System
We have a uniform rod of length \( l \) and mass \( 2m \) resting on a smooth horizontal table. A point mass \( m \) is moving horizontally at a right angle to the rod with velocity \( v \) and collides with one end of the rod.

### Step 2: Conservation of Linear Momentum
Before the collision, the linear momentum of the system is given by the momentum of the point mass:
\[
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