SATHEE: Rotation 2 Question 1

Rotation 2 Question 1

1. 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) $36 \hat{k}$

(b) $- 34 (\hat{k} - \hat{i})$

(d) $48 (\hat{i} + \hat{j})$

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Answer:

Correct Answer: 1. (c)

Solution:

Position of particle is, $r = 2 t \hat{i} - 3 t^{2} \hat{j}$

where, $t$ is instantaneous time.

Velocity of particle is

$v = \frac{d r}{d t} = 2 \hat{i} - 6 \hat{t} j$

Now, angular momentum of particle with respect to origin is given by

$\begin{matrix} L = m (r \times v) \\ = m (2 t \hat{i} - 3 t^{2} \hat{j}) \times (2 \hat{i} - 6 t \hat{j}) \end{matrix}$

As, $\hat{i} \times \hat{i} = \hat{j} \times \hat{j} = 0$

$\Rightarrow L = m (- 12 t^{2} \hat{k} + 6 t^{2} \hat{k})$

As, $\hat{i} \times \hat{j} = \hat{k}$ and $\hat{j} \times \hat{i} = - \hat{k}$

$\Rightarrow L = - m (6 t^{2}) \hat{k}$

So, angular momentum of particle of mass $2 k g$ at time $t = 2 s$ is

$L = (- 2 \times 6 \times 2^{2}) \hat{k} = - 48 \hat{k}$

Rotation 2 Question 1

1. 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

Answer:

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Rotation 2 Question 1

1. 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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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1. 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