A particle of mass M=0.2 kg is initially at rest in the xy-plane at a point x=−l, y=−h, where l=10 m and h=1 m....

A particle of mass

M = 0.2 kg

is initially at rest in the

x y

-plane at a point

(x = - l, y = - h)

, where

l = 10 m

and

h = 1 m

. The particle is accelerated at time

t = 0

with a constant acceleration

a = 10 m s^{- 2}

along the positive

x

-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by

\vec{L}

and

\vec{τ}

, respectively.

\hat{i}, \hat{j}

and

\hat{k}

are unit vectors along the positive

x, y

and

z

-directions, respectively. If

\hat{k} = \hat{i} \times \hat{j}

then which of the following statement(s) is (are) correct?

The particle arrives at the point

(x = l, y = - h)

at time

t = 2 s

\vec{τ} = 2 \hat{k}

when the particle passes through the point

(x = l, y = - h)

\vec{L} = 4 \hat{k}

when the particle passes through the point

(x = l, y = - h)

\vec{τ} = \hat{k}

when the particle passes through the point

(x = 0, y = - h)

Solution:

At $(t = 2 s) :$

displacement along $+ X$ axis

$= \frac{1}{2} \times (10) \times t^{2}$

$= \frac{1}{2} \times 10 \times 4 = 20 m$

Hence, particle arrives at $(10, - 1)$

At $(x = l, y = - h)$ ,

$\vec{τ} = \vec{r} \times \vec{F}$

$= (10 \hat{i} - \hat{j}) \times \{0 .2 \times 10\} \hat{i}$ $= (2 \hat{k}) N m$

$\vec{L} = \vec{r} \times \vec{p}$ $= (10 \hat{i} - \hat{j}) \times \{0 .2 \times v \hat{i}\}$

and $v (at t = 2 s) = 0 + 10 \times 2 = 20 m s^{- 1}$

$∴ \vec{L} = (10 \hat{i} - \hat{j}) \times 4 \hat{i} = (4 \hat{k}) N m s$

At $(x = 0, y = - h) :$

$\vec{r} = 0 \hat{i} - \hat{j}$

$\vec{F} = 2 \hat{i}$

$∴ \vec{τ} = \vec{r} \times \vec{F} = (2 \hat{k}) N m$

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A particle of mass M=0.2 kg is initially at rest in the xy-plane at a point x=−l, y=−h, where l=10 m and h=1 m....

Ranking

Find Colleges

Compare Colleges

Exams

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Course Finder

Your Gateway to Top Colleges & Exams

IIT Madras

IIT Delhi

IIT Bombay

IIT Kanpur

IIT Kharagpur

IIT Roorkee

IIT Guwahati

IIT Hyderabad

IIT BHU

IIT Dhanbad

IIT Indore

IIT Gandhinagar

IIT Ropar

IIT Jodhpur

IIT Mandi

IIT Patna

Top Exams

A particle of mass M=0.2 kg is initially at rest in the xy-plane at a point x=−l, y=−h, where l=10 m and h=1 m....

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