Question

A particle acted by constant forces $4\hat{i}+\hat{j}-3\hat{k}$ and $3\hat{i}+\hat{j}-\hat{k}$ is displaced from the point $\hat{i}+2\hat{j}+3\hat{k}$ to the point $5\hat{i}+4\hat{j}+\hat{k}$, then the total work done by the forces is

• A. $10$
• B. $20$
• C. $40$
• D. $Noneofthese$

Answer 1

Answer: (C)

$40$

Total force ${\overline{F}}_1+{\overline{F}}_2=\overline{F}=7\hat{i}+2\hat{j}-4\hat{k}$

And displacement $\overline{d}=(5\hat{i}+4\hat{j}+\hat{k})-(\hat{i}+2\hat{j}+3\hat{k})=4\hat{i}+2\hat{j}-2\hat{k}$

$\therefore$ Work done $=\overline{F}\cdot \overline{d}$

$=(7\hat{i}+2\hat{j}-4\hat{k})\cdot (4\hat{i}+2\hat{j}-2\hat{k})$
$=28+4+8=40$ units