Question

A body constrained to move along the $z$-axis of a co-ordinate system is subjected to a constant force $\overrightarrow{F}=(-\hat{i}+2\hat{j}+3\hat{k})\text{N}$. What is the work done by the force in moving the body over a distance of $4\text{m}$ along the $z$-axis?

• A. $6\text{J}$
• B. $8\text{J}$
• C. $16\text{J}$
• D. $12\text{J}$

Answer 1

The correct option is D $12\text{J}$

Given $\overrightarrow{F}=(-\hat{i}+2\hat{j}+3\hat{k})\text{N}$
Since the body is constrained to move along the $z$ - axis over a distance of $4\text{m}$
$\therefore \overrightarrow{S}=\left(4\hat{k}\right)\text{m}$
Then, Work done, $W$ $=\overrightarrow{F}.\overrightarrow{S}$
$\Rightarrow W=(-\hat{i}+2\hat{j}+3\hat{k}).\left(4\hat{k}\right)$
$\Rightarrow W=12\text{J}$