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

Question

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]

Smart Achievers · Accepted Answer

(40)

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

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

$W = 40 J$

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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Solution

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

Ans. (40) W=F→ (r→f-r→i) =(5i^+2j^+7k^)·[(5i^-2j^+k^)-(2i^+3j^-4k^)] W=40 J

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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)

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

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

$W = 40 J$