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

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Rotational Mechanics

The time dependence of the position of a particle of mass

m = 2

is given by

r (t) = 2 t \hat{i} - 3 t^{2} \hat{j}

Its angular momentum with respect to the origin at time

t = 2

is .

(A) $- 48 \hat{k}$ ✓ Correct
(B) $48 (\hat{i} + \hat{j})$
(C) $36 \hat{k}$
(D) $- 34 (\hat{k} - \hat{i})$

Answer: (A)

Solution

Angular momentum about the origin is

L = m (r \times v)

. Differentiating the position,

v = 2 \hat{i} - 6 t \hat{j}

, so at

t = 2

we have

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

and

v = 2 \hat{i} - 12 \hat{j}

. Their cross product points along

\hat{k}

with magnitude

(4) (- 12) - (- 12) (2) = - 48 + 24 = - 24

, so

r \times v = - 24 \hat{k}

. Multiplying by the mass

m = 2

gives

L = - 48 \hat{k}

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option

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