The time dependence of the position of a particle of mass m=2 is given by  \vec{r}\left ( t \right )= 2t\hat{i}-3t^{2}\hat{j} Its angular momentum with respect to the origin , at time t=2is:

 

 

  • Option 1)

    48\left ( \hat{i +\hat{j}} \right )

  • Option 2)

    36\hat{k}

  • Option 3)

    -34\left ( \hat{k} -\hat{i}\right )

  • Option 4)

    -48\hat{k}

Answers (1)

\vec{r}=2t\hat{i}-3t^{2}\hat{t}

m=2kg

\vec{L}=m \left [ \hat{r}\times \hat{v} \right ]

\vec{v}=\frac{d\left ( \vec{r} \right )}{dt}

at t=2sec

\vec{V}=2\hat{i}-12\hat{j}

\vec{r } =4\hat{i}-12\hat{j}

\left [ \vec{r}\times \vec{v}\right ]=\left ( 4\hat{i} -12\hat{j}\right )\times \left ( 2\hat{i}-12 \hat{j}\right )=-24\hat{k}

\vec{L}=m \left [ \vec{r}\times \vec{v} \right ]

\vec{L}=-48\hat{K}


Option 1)

48\left ( \hat{i +\hat{j}} \right )

Option 2)

36\hat{k}

Option 3)

-34\left ( \hat{k} -\hat{i}\right )

Option 4)

-48\hat{k}

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