Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

A system of particles has initial angular momentum \( \mathbf{L}(0) = (\hat{i} + 2\hat{j} + 5\hat{k})\text{ kg m}^2/\text{s} \). It is subjected to a time-varying net external torque \( \boldsymbol{\tau}_{\text{ext}}(t) = (4t\hat{i} + 2\hat{j})\text{ N m} \). The magnitude of the total angular momentum of the system at \( t = 2\text{ s} \) is:

1. A
   \( \sqrt{125}\text{ kg m}^2/\text{s} \)
2. B
   \( \sqrt{166}\text{ kg m}^2/\text{s} \)
3. C
   \( \sqrt{142}\text{ kg m}^2/\text{s} \)
4. D
   \( 12\text{ kg m}^2/\text{s} \)