Position vector of 1,kg object is overrightarrow{ r }=(3 hat{ i }-hat{ j }),m and its velocity overr

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6.System of Particles and Rotational Motion

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The position vector of $1\,kg$ object is $\overrightarrow{ r }=(3 \hat{ i }-\hat{ j })\,m$ and its velocity $\overrightarrow{ v }=(3 \hat{ j }+ k )\,ms ^{-1}$. The magnitude of its angular momentum is $\sqrt{ x } Nm$ where $x$ is

A

$89$

B

$91$

C

$90$

D

$95$

(JEE MAIN-2022)

Solution

Using $\overrightarrow{ L }=\overrightarrow{ r } \times \overrightarrow{ p }=\overrightarrow{ r } \times m \overrightarrow{ v }, m =1\,kg$

$\overrightarrow{ L }=(3 \hat{ i }-\hat{ j }) \times(3 \hat{ j }+\hat{ k })=(9 \hat{ k }-3 \hat{ j }-\hat{ i })\,N – s$

$\Rightarrow|\overline{ L }|=\sqrt{91}\,N – s$

Standard 11

Physics

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