Question

A force $(4\hat{i}+\hat{j}-2\hat{k})\text{N}$ acting on a body maintains its velocity at $(2\hat{i}+3\hat{j}-\hat{k})\text{m/s}$. The power exerted is

• A. $15\text{W}$
• B. $13\text{W}$
• C. $12\text{W}$
• D. $20\text{W}$

Answer 1

The correct option is B $13\text{W}$

We have force $\overrightarrow{F}=(4\hat{i}+\hat{j}-2\hat{k})\text{N}$
Velocity,$\overrightarrow{v}=(2\hat{i}+3\hat{j}-\hat{k})\text{m/s}$
Therefore, Power is given by $P=\overrightarrow{F}.\overrightarrow{v}=(4\hat{i}+\hat{j}-2\hat{k}).(2\hat{i}+3\hat{j}-\hat{k})$
$\Rightarrow P=(8+3+2)\text{W}$
$\Rightarrow P=13\text{W}$