A small particle of mass


A small particle of mass $\mathrm{m}$ is projected at an angle $\theta$ with the $\mathrm{x}$-axis with an initial velocity $\mathrm{v}_{0}$ in the $x-y$ plane as shown in the figure. At a time $t<\frac{v_{0} \sin \theta}{g}$, the angular momentum of the particle is: Where $\hat{i}, \hat{j}$ and $\hat{k}$ are unit vectors along $x, y$ and $z$-axis respectively.

  1. $\frac{1}{2} m g v_{0} t^{2} \cos \theta \hat{i}$

  2. $-m g v_{0} t^{2} \cos \theta \hat{j}$

  3. $m g v_{0} t \cos \theta \hat{k}$

  4. $-\frac{1}{2} m g \mathrm{v}_{0} \mathrm{t}^{2} \cos \theta \hat{\mathrm{k}}$

Correct Option: , 4


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