Question

A force $\overrightarrow{F}=3\hat{i}+c\hat{j}+2\hat{k}$ acting on a particle causes a displacement $\overrightarrow{S}=-4\hat{i}+2\hat{j}-3\hat{k}$ in its own direction. If the work done by the force is $6\text{J}$, then the value of $c$ will be

• A. $12$
• B. $1$
• C. $6$
• D. $0$

Answer 1

The correct option is A $12$

Workdone $=\overrightarrow{F}.\overrightarrow{S}=6J$
Given $\overrightarrow{F}=(3i+cj+2k)\text{N}$
$\overrightarrow{S}=(-4i+2j-3k)m$
$W=\overrightarrow{F}.\overrightarrow{S}=6$
$\Rightarrow 3(-4)+c\left(2\right)+2(-3)=6$
$\Rightarrow -12+2c-6=6$
$\Rightarrow 2c=24$
$c=12$