A small particle of mass $m$ is projected at an angle $\theta$ with the x-axis with an initial velocity $\mathrm { v } _ { 0 }$ in the $\mathrm { x } - \mathrm { y }$ plane as shown in the figure. At a time $t < \frac { v _ { 0 } \sin \theta } { g }$, the angular momentum of the particle is where $\hat { \mathrm { i } } , \hat { \mathrm { j } }$ and $\hat { \mathrm { k } }$ are unit vectors along $\mathrm { x } , \mathrm { y }$ and z-axis respectively. (1) $- \mathrm { mgv } _ { 0 } \mathrm { t } ^ { 2 } \cos \theta \hat { \mathrm { j } }$ (2) $\mathrm { mgv } _ { 0 } t \cos \theta \hat { \mathrm { k } }$ (3) $- \frac { 1 } { 2 } m g v _ { 0 } t ^ { 2 } \cos \theta \hat { k }$ (4) $\frac { 1 } { 2 } m g v _ { 0 } t ^ { 2 } \cos \theta \hat { i }$
A small particle of mass $m$ is projected at an angle $\theta$ with the x-axis with an initial velocity $\mathrm { v } _ { 0 }$ in the $\mathrm { x } - \mathrm { y }$ plane as shown in the figure. At a time $t < \frac { v _ { 0 } \sin \theta } { g }$, the angular momentum of the particle is where $\hat { \mathrm { i } } , \hat { \mathrm { j } }$ and $\hat { \mathrm { k } }$ are unit vectors along $\mathrm { x } , \mathrm { y }$ and z-axis respectively.\\
(1) $- \mathrm { mgv } _ { 0 } \mathrm { t } ^ { 2 } \cos \theta \hat { \mathrm { j } }$\\
(2) $\mathrm { mgv } _ { 0 } t \cos \theta \hat { \mathrm { k } }$\\
(3) $- \frac { 1 } { 2 } m g v _ { 0 } t ^ { 2 } \cos \theta \hat { k }$\\
(4) $\frac { 1 } { 2 } m g v _ { 0 } t ^ { 2 } \cos \theta \hat { i }$