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NEET Sample Paper NEET Sample Test Paper-89

  • question_answer
    A particle of mass 2 kg is moving such that at time t, its position, in meter, is given by \[\overrightarrow{r}(t)=5\hat{i}-2{{t}^{2}}\hat{j}.\] The angular momentum of the particle at t = 2s about the origin in \[kg\,\,{{m}^{-2}}{{s}^{-1}}\]

    A) \[-80\,\hat{k}\]  

    B)        \[(10\hat{i}-16\hat{j})\]

    C) \[-40\,\hat{k}\]  

    D)        \[40\hat{k}\]

    Correct Answer: A

    Solution :

    [a] Angular momentum L\[=m(\overrightarrow{r}\times \overrightarrow{v})\] \[=2kg\left( \overrightarrow{r}\times \frac{d\overrightarrow{r}}{dt} \right)=2kg(5\hat{i}-2{{t}^{2}}\hat{j})\times (-4\,t\hat{j})\] \[=2kg(-20\,t\,\hat{k})=2\,kg\times -20\times 2\,{{m}^{-2}}{{s}^{-1}}\hat{k}\] \[=-80\,\hat{k}\]


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