A particle moves from a point - r 1-2 m - i -3 m - j to another point - r 2-3 m - i -2 m - j acts on it- Find the work done by the force on the particleduring the displacement-

Initial position vector, r1 #8594;=2i #8594;+3j #8594; Final position vector, r #8594;2=3i #8594;+2j #8594; So, displacement vector, r #8594;=r ...

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Byju's Answer

Standard IX

Physics

Work

A particle mo...

Question

A particle moves from a point ${\underset{r}{\to}}_{1} = (2 m) \underset{i}{\to} + (3 m) \underset{j}{\to}$ to another point ${\underset{r}{\to}}_{2} = (3 m) \underset{i}{\to} + (2 m) \underset{j}{\to}$ acts on it. Find the work done by the force on the particle during the displacement.

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Solution

Initial position vector,
$\vec{r_{1}} = 2 \vec{i} + 3 \vec{j}$
Final position vector,
${\vec{r}}_{2} = 3 \vec{i} + 2 \vec{j}$
So, displacement vector,
$\vec{r} = {\vec{r}}_{2} - {\vec{r}}_{1} = (3 \vec{i} + 2 \vec{j}) - (2 \vec{i} + \vec{j}) = \vec{i} - \vec{j} Force acting on the particle, \vec{F} = 5 \vec{i} + 5 \vec{j} So, work done = \vec{F} \cdot \vec{S} = 5 \times 1 + 5 (- 1) = 0$

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A particle moves from a point →r1=2 m →i+3 m →j to another point →r2= 3 m →i+2 m →j acts on it. Find the work done by the force on the particle during the displacement.

Initial position vector, r1→=2i→+3j→ Final position vector, r→2=3i→+2j→ So, displacement vector, r→=r→2-r→1=3i→+2j→-2i→+j→=i→-j→Force acting on the particle, F→=5i→+5j→So, work done=F→·S→=5×1+5 -1=0

A particle moves from a point ${\underset{r}{\to}}_{1} = (2 m) \underset{i}{\to} + (3 m) \underset{j}{\to}$ to another point ${\underset{r}{\to}}_{2} = (3 m) \underset{i}{\to} + (2 m) \underset{j}{\to}$ acts on it. Find the work done by the force on the particle during the displacement.