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A small particle of mass \( m \) is projected at an angle \( \theta \) with the \( x \)-axis with an initial velocity \( v_{0} \) in the \( x-y \) plane as shown in the figure. At a time \( t\left(v_{0} \sin \theta / g\right) \), the angular momentum of the particle is
(1) \( -m g v_{0} t^{2} \cos \theta \hat{j} \)
(2) \( m g v_{0} t \cos \theta \hat{k} \)
(3) \( -\frac{1}{2} m g v_{0} t^{2} \cos \theta \hat{k} \)
(4) \( \frac{1}{2} m g v_{0} t^{2} \cos \theta \hat{i} \)
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