PYQ NEET- Work Energy And Power L-10

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

A) $8 \mathrm{~J}$

B) $11 \mathrm{~J}$

C) $5 \mathrm{~J}$

D) $2 \mathrm{~J}$

Answer: $5 \mathrm{~J}$#

Solution:#

$$ \begin{alignedat} & \text { Here } \overrightarrow{r_1}=(-2 \hat{i}+5 \hat{j}) m \ & \overrightarrow{r_2}=(-4 \hat{j}+3 \hat{k}) m \ & \vec{F}=(4 \hat{i}+3 \hat{j}) N \end{aligned} $$

Work done by force $\mathrm{F}$ in moving from $\overrightarrow{r_1}$ to $\overrightarrow{r_2}$ $$ \begin{alignedat} & W=\vec{F}\cdot\left(\overrightarrow{r_2}-\overrightarrow{r_1}\right) \ & \Rightarrow W=(4 \hat{i}+3 \hat{j})(2 \hat{i}-\hat{j}+3 \hat{k}) & \Rightarrow W=(4 \hat{i}+3 \hat{j}) \cdot(2 \hat{i}-\hat{j}+3 \hat{k}) \ & \Rightarrow W=8+(-3)=5 J \end{aligned} $$