question_answer

A small particle of mass m is projected at an angle\[\theta \]with the x-axis with an initial velocity v0 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 -                  [AIEEE 2010]

A)   \[\frac{1}{2}mg{{v}_{0}}{{t}^{2}}\cos \theta \hat{i}\]

B)        \[-mg{{v}_{0}}{{t}^{2}}\cos \theta \hat{j}\]

C)   \[mg{{v}_{0}}t\cos \theta \hat{k}\]

D)       \[-\frac{1}{2}mg{{v}_{0}}{{t}^{2}}\cos \theta \hat{k}\]

Correct Answer: D

Solution :

[d] at any time t

So,

where\[\hat{i},\hat{j}\]and\[\hat{k}\]are unit vectors along\[x,y\] and z-axis respectively.