The time dependence of the position of a particle of mass m = 2 is given by r(t) = 2ti - 3t²j. Its angular momentum, with respect to the origin, at time t = 2 is (a) 36 k (b) - 48 k (c) -34(k - i) (d) 48(i + j)

Answer: (b). v=(d r)/(dt)=2 i-6t j. At t=2: r=4 i-12 j, v=2 i-12 j. L=m( r× v)=2[(4)(-12)-(-12)(2)] k L=2(-48+24) k=-48 k So the answer is (b) -48 k.

The time dependence of the position of a particle of mass m = 2 is… | JEE Main 2019 (10 Apr, Shift 2)

Q59JEE Main 2019 · 10 APR · SHIFT 2Medium

Angular Momentum & its Conservation

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

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Answer: (b)

$\vec v=\frac{d\vec r}{dt}=2\hat i-6t\hat j$ . At $t=2$ : $\vec r=4\hat i-12\hat j$ , $\vec v=2\hat i-12\hat j$ .
$\vec L=m(\vec r\times\vec v)=2[(4)(-12)-(-12)(2)]\hat k$
$\vec L=2(-48+24)\hat k=-48\hat k$
So the answer is (b) $-48\hat k$ .

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Angular Momentum & its Conservation question from JEE Main 2019 (10 Apr, Shift 2)

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