Question

A particle gets displaced by
$\Delta \bar{r}=\left(2\hat{i}+3\hat{j}+4\hat{k}\right)m$ under the action of a force
$\vec{F}=\left(7\hat{i}+4\hat{j}+3\hat{k}\right).$ The change in its kinetic energy is

• A. $38\,J$
• B. $70\,J$
• C. $52.5\,J$
• D. $1.26\,J$

Answer 1

Answer: (A)

According to work-energy theorem, Change in kinetic energy = work done
$=\overrightarrow{F}.\Delta \vec{r}=\left(7\hat{i}+4\hat{j}+3\hat{k}\right)\cdot\left(2\hat{i}+3\hat{j}+4\hat{k}\right)$
$= 14+ 12+12 = 38\, J$