A small particle moves to position from its initial position under the action of force The value of work done will be _________ J. [2023]

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Solution

Q.
A small particle moves to position $5 \hat{i} - 2 \hat{j} + \hat{k}$ from its initial position $2 \hat{i} + 3 \hat{j} - 4 \hat{k}$ under the action of force $5 \hat{i} + 2 \hat{j} + 7 \hat{k} N .$ The value of work done will be _________ J. [2023]

Ans.
(40)

$W = \vec{F} ({\vec{r}}_{f} - {\vec{r}}_{i})$

$= (5 \hat{i} + 2 \hat{j} + 7 \hat{k}) \cdot [(5 \hat{i} - 2 \hat{j} + \hat{k}) - (2 \hat{i} + 3 \hat{j} - 4 \hat{k})]$

$W = 40 J$

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