Question

Two forces $\overrightarrow{F_1}=\hat{i}-2\hat{j}+2\hat{k}$ $\text{N}$ and $\overrightarrow{F_2}=-3\hat{i}+\hat{j}-3\hat{k}$ $\text{N}$ acts on a body and causes it to displace from position $\overrightarrow{s_1}=\hat{i}-\hat{j}$ $\text{m}$ to $\overrightarrow{s_2}=2\hat{j}-a\hat{k}$ $\text{m}$. Find the value of ${}^{\prime }{a}^{\prime }$ if the amount of net work done by the forces is $5\text{J}$ during the displacement.

• A. $-4$
• B. $8$
• C. $6$
• D. $-5$

Answer 1

The correct option is C $6$

Net force acting of body is given by:
$\overrightarrow{F}=\overrightarrow{F_1}+\overrightarrow{F_2}=\left(\hat{i}-2\hat{j}+2\hat{k}\right)+(-3\hat{i}+\hat{j}-3\hat{k})\Rightarrow \overrightarrow{F}=-2\hat{i}-\hat{j}-\hat{k}$
Displacement of body while moving from initial to final position:

$\overrightarrow{S}=\overrightarrow{s_2}-\overrightarrow{s_1}=(2\hat{j}-a\hat{k})-\left(\hat{i}-\hat{j}\right)\Rightarrow \overrightarrow{S}=-\hat{i}+3\hat{j}-a\hat{k}m$
Work done by force given by:
$W=\overrightarrow{F}.\overrightarrow{S}$
$W=(-2\hat{i}-\hat{j}-\hat{k}).(-\hat{i}+3\hat{j}-a\hat{k})\Rightarrow 5=(2-3+a)\Rightarrow a=6$