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JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Afternoon)

  • question_answer
                The time dependence of the position of a particle of mass \[m=2\]is given by \[\vec{r}(t)=2t\hat{i}-3{{t}^{2}}\hat{j}.\] Its angular momentum, with respect to the origin, at time \[t=2\]is : [JEE Main 10-4-2019 Afternoon]

    A) \[36\hat{k}\]                           

    B) \[-34(\hat{k}-\hat{i})\]

    C) \[48(\hat{i}+\hat{j})\]                       

    D) \[-48\hat{k}\]

    Correct Answer: D

    Solution :

    \[\vec{L}=m[\vec{r}\times \vec{v}]\]           \[m=2kg\]           \[\vec{r}=2t\,\hat{i}-3{{t}^{2}}\hat{j}\]           \[=4\,\hat{i}-12\hat{j}\,(At\,t=2\,sec)\]           \[\text{\vec{v}=}\frac{d\vec{r}}{dt}=2\hat{i}-6t\,\hat{j}=2\hat{i}-12\hat{j}\]           \[\text{\vec{r}}\times \text{\vec{v}}\,\text{=(4}\hat{i}-12\,\hat{j})\times (2\hat{i}-12\hat{j})\]           \[=-24\hat{k}\]           \[\vec{L}=m(\vec{r}\times \vec{v})\]           \[=-48\hat{k}\]


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