Two particles of mass m & 2m have velocities `u hat( j) ` & `u hat( i ) ` respectively . They collide completely inelastically. Find the loss in kinetic energy of the system.

Options

A. `m u^(2)`
B. `(2)/(3) m u^(2)`
C. `( m u^(2))/( 4)`
D. `( m u^(2))/( 4)`

Explanation

To solve the problem of finding the loss in kinetic energy during a completely inelastic collision between two particles, we can follow these steps:

### Step 1: Determine the Initial Kinetic Energy
The two particles have masses \( m \) and \( 2m \) with velocities \( \mathbf{u} \hat{j} \) and \( \mathbf{u} \hat{i} \) respectively.

- For the particle of mass \( m \) moving with velocity \( \mathbf{u} \hat{j} \):
\[
KE_1 = \frac{1}{2} m u^2
...