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  • A particle of mass 2kg is moving such that at time t,its position, in meter, is given by <img alt="\overrightarrow{r}(t)=5\overset{\wedge }{i}-2t^{2}\overset{\wedge }{j}." src="https://learn.c

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

Option: 1

-80\overset{\wedge }{k}


Option: 2

\left ( 10\overset{\wedge }{i}-16\overset{\wedge }{j} \right )


Option: 3

-40\overset{\wedge }{k}


Option: 4

40\overset{\wedge }{k}


Answers (1)

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\vec{P}=m \vec{v}=m \frac{d \vec{r}}{d t}=2(-4 t) \hat{j}=-16 \hat{j}$\\ (putting $t=2$)\\ $\vec{r}=5 \hat{i}-8 \hat{j}$\\ $\vec{L}=\vec{r} \times \vec{p}$\\ Substituting. $\vec{L}=(5 \hat{i}-8 \hat{j}) \times(-16 \hat{j})$ $\vec{L}=-80 \hat{k}

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