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Work, Energy, and Power — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWork, Energy, and Power2 Marks
Question
A particle moves from a point $\vec{\text{r}}_1=(2\text{m})\vec{\text{i}}+(3\text{m})\vec{\text{j}}$ to another point $\vec{\text{r}}_2=(3\text{m})\vec{\text{i}}+(2\text{m})\vec{\text{j}}$ during which a certain force $\vec{\text{F}}=(5\text{N})\vec{\text{i}}+(5\text{N})\vec{\text{j}}$ acts on it. Find the work done by the force on the particle during the displacement.
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Answer

Given, $\vec{\text{r}}_1=2\hat{\text{i}}+3\hat{\text{j}}$ $\vec{\text{r}}_2=3\hat{\text{i}}+2\hat{\text{j}}$ So, displacement vector is given by, $\vec{\text{r}}=\vec{\text{r}}_1-\vec{\text{r}}_2$ $\Rightarrow\vec{\text{r}}=\Big(3\hat{\text{i}}+2\hat{\text{j}}\Big)-\Big(2\hat{\text{i}}+3\hat{\text{j}}\Big)$ $=\hat{\text{i}}-\hat{\text{j}}$ So, work done $=\vec{\text{F}}\times\vec{\text{S}}$ $=5\times1+5(-1)=0$

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