The time dependence of the position of a particle of mass m=2 is given by r →t=2t i^-3t^2j^ . Its angular momentum, with respect to the origin, at time t=2 is:

Correct answer: (C) -48 k^. r→=2t i^-3t^2 j^ v→=2 i^-6t j^ Momentum p→=mv→ =4 i^-12t j^ ∴ angular momentum L→=r→×p→ =2t i^-3t^2 j^×4 i^-12t j^ =-24t^2 k^+12t^2 k^ =-12t^2 k^ At time t=2 L→=-48 k^

Q80 / 90 · JEE Main 2019 (10 Apr Shift 2) · Physics

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:

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

Solution

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

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

Momentum

\vec{p} = m \vec{v}

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

∴

angular momentum

\vec{L} = \vec{r} \times \vec{p}

= (2 t \hat{i} - 3 t^{2} \hat{j}) \times (4 \hat{i} - 12 t \hat{j})

= - 24 t^{2} \hat{k} + 12 t^{2} \hat{k}

= - 12 t^{2} \hat{k}

At time

t = 2

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

Hence, the correct answer is option: 'C'.

Relevant Questions

When the position vector changes sign as , which one of the following vector will not flip under sign change ?28 Jan, 2026 (E)Angular momentum and Angular impulse
A thin uniform rod of mass and length is pivoted at a height as shown in the figure. The rod is allowed to fall from a vertical position and24 Jan, 2026 (E)Angular momentum and Angular impulse
Two small balls with masses and 2 m are attached to both ends of a rigid rod of length and negligible mass. If angular momentum of this syst23 Jan, 2026 (M)Angular momentum and Angular impulse
Two cars and each of mass are moving on parallel tracks separated by a distance of 10 m, in same direction with speeds and . The magnitude o21 Jan, 2026 (E)Angular momentum and Angular impulse
If and represent the angular momentum and linear momentum respectively of a particle of mass ' m ' having position vector . The direction of04 Apr, 2025 (M)Angular momentum and Angular impulse
A solid sphere with uniform density and radius R is rotating initially with constant angular velocity about its diameter. After some time du04 Apr, 2025 (E)Angular momentum and Angular impulse

The time dependence of the position of a particle of mass m=2 is given by r →t=2t i^-3t2j^ . Its angular momentum, with respect to the origin, at time t=2 is:

Solution

Relevant Questions

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: