Question

A block is displaced from (1m, 4m, 6m) to $(2\hat{i}+3\hat{j}-4\hat{k})$ m under a constant force $\overrightarrow{F}=(6\hat{i}-2\hat{j}+\hat{k})N.$ Find the work done by this force.

• A. -1 J
• B. -2 J
• C. -3 J
• D. -5 J

Answer 1

Answer: (B)

-2 J

Displacement vector $\overrightarrow{s}$ is given by $\overrightarrow{r_2}-\overrightarrow{}$

$⟹\overrightarrow{s}=(2-1)\hat{i}+(3-4)\hat{j}+(-4-6)\hat{k}$

$=\hat{i}-\hat{j}-10\hat{k}$

Thus work done by force $F$ is $\overrightarrow{F}.\overrightarrow{s}$

$=(6\hat{i}-2\hat{j}+\hat{k}).(\hat{i}-\hat{j}-10\hat{k})J$

$=(6+2-10)J=-2J$