A particle moves from a point to when a force of N is applied. How much work has been done by the force? [2016]

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Solution

Q.
A particle moves from a point $(- 2 \hat{i} + 5 \hat{j})$ to $(4 \hat{j} + 3 \hat{k})$ when a force of $(4 \hat{i} + 3 \hat{j})$ N is applied. How much work has been done by the force [2016]

1 8 J

2 11 J

3 5 J

4 2 J

Ans.
(3)

Here ${\vec{r}}_{1} = (- 2 \hat{i} + 5 \hat{j}) m,$ ${\vec{r}}_{2} = (4 \hat{j} + 3 \hat{k}) m$

$\vec{F} = (4 \hat{i} + 3 \hat{j}) N,$ $W = ?$

Work done by force $F$ in moving from ${\vec{r}}_{1}$ to ${\vec{r}}_{2},$

$W = \vec{F} \cdot ({\vec{r}}_{2} - {\vec{r}}_{1}) \Rightarrow W = (4 \hat{i} + 3 \hat{j}) \cdot (4 \hat{j} + 3 \hat{k} + 2 \hat{i} - 5 \hat{j})$

$= (4 \hat{i} + 3 \hat{j}) \cdot (2 \hat{i} - \hat{j} + 3 \hat{k}) = 8 + (- 3) = 5 J$

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