Question

A force of magnitude of $30N$ acting along $\hat{i}+\hat{j}+\hat{k}$, displaces a particle from a point $(2,4,1)$ to $(3,5,2)$. The work done during this displacement is:

• A. $90J$
• B. $30J$
• C. $\frac{30}{\sqrt{3}}J$
• D. $20J$

Answer 1

The correct option is B $30J$

$Work=\overline{F}.ds$

$\Rightarrow ds=(3\hat{i}+5\hat{j}+2\hat{k})-(2\hat{i}+4\hat{j}+\hat{k})$

$\Rightarrow ds=\hat{i}+\hat{j}+\hat{k}$

Since force is acting along $\hat{i}+\hat{j}+\hat{k}$

$\Rightarrow Work=30\times \frac{(\hat{i}+\hat{j}+\hat{k})}{\sqrt{3}}$

$\Rightarrow Work=30\times \frac{\sqrt{3}}{\sqrt{3}}$

$\Rightarrow Work=30$