Question

A body constrained to move in $z$ direction is subjected to a force given by $\overrightarrow{F}=(3\hat{i}-10\hat{j}+5\hat{k})\text{N}.$ What is the work done by this force in moving the body through a distance of $5\text{m}$ along $z-$axis?

• A. $15\text{J}$
• B. $15\text{J}$
• C. $-50\text{J}$
• D. $25\text{J}$

Answer 1

The correct option is D $25\text{J}$

As work done is dot product of force and displacement, we get
$W=\overrightarrow{F}.\overrightarrow{S}=(3\hat{i}-10\hat{j}+5\hat{k}).5\hat{k}$
$W=25\text{J}$

Why this question ? "Understanding of work done by a constant force(Vector) as sum of products of components of $\overrightarrow{F}$ and $\overrightarrow{S}$ along axes" "Caution : Work is dot product of $\overrightarrow{F}$ and $\overrightarrow{S}$ not just product of their magnitudes "