AIEEE Solved Paper-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 :
where\[\hat{i},\hat{j}\]and\[\hat{k}\]are unit vectors along\[x,y\] and z-axis respectively. at any time t \[\overrightarrow{r}=({{v}_{0}}cos\theta )t\hat{i}+\left( ({{v}_{0}}\sin \theta )t-\frac{1}{2}g{{t}^{2}} \right)\hat{j}\] \[\overrightarrow{v}={{v}_{0}}\cos \theta \hat{i}+({{v}_{0}}\sin \theta -gt)\hat{j}\] So, \[\overrightarrow{L}=m(\overrightarrow{r}\times \overrightarrow{v})=-\frac{1}{2}mg{{v}_{0}}{{t}^{2}}\cos \theta \hat{k}\]
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