Question

A particle of mass $0.5kg$ is displaced from position $(2,3,1)\text{to}(4,3,2)$ by applying a force of magnitude $30N$, acting along $(\hat{i}+\hat{j}+\hat{k})$. The work done by the force is-

• A. $10\sqrt{3}J$
• B. $30\sqrt{3}J$
• C. $30J$
• D. None of these

Answer 1

The correct option is B $30\sqrt{3}J$

Given $\overrightarrow{F}=30\frac{(\hat{i}+\hat{j}+\hat{k})}{\sqrt{3}}$
Initial position vector $\overrightarrow{r_i}=(2\hat{i}+3\hat{j}+\hat{k})$
Final position vector $\overrightarrow{r_f}=(4\hat{i}+3\hat{j}+2\hat{k})$
Displacement vector
$\Delta \overrightarrow{r}=2\hat{i}+\hat{k}$
Work Done by the force is
$W=\overrightarrow{F}.\Delta \overrightarrow{r}=30\sqrt{3}J$