Question

Two constant force ${\overrightarrow{F}}_{1}and{\overrightarrow{F}}_2$ acts on a body.these forces displaces the body from point P(1, -2, 3) to Q (2, 3, 7 ) in 2s starting from rest.force ${\overrightarrow{F}}_1$ is of magnitude 9 N and acting along vector $(2\hat{i}-2\hat{j}+\hat{k})$ . the positions are in meter. find work done by ${\overrightarrow{F}}_1$.

• A. $-12J$
• B. $+12J$
• C. $36J$
• D. $-36J$

Answer 1

Answer: (A)

$-12J$

$\begin{array}{cc}{\overrightarrow{F}}_1& =k(2\hat{i}-2\hat{ȷ}+\hat{k})\\ \overrightarrow{d}=& (2-1)\hat{1}+(3-(-2\left)\right)\hat{j}\\ & +(7-3)\hat{k}\\ =& \left(1\right)\hat{1}+\left(5\right)\hat{j}+\left(4\right)\hat{k}\\ {\overrightarrow{W}}_1=& {\overrightarrow{F}}_1\cdot \overrightarrow{d}\\ & =k(2\hat{i}-2\hat{j}+\hat{k})\cdot (i+5\hat{j}+4\hat{k})......\left(i\right)\end{array}$

$|{\overrightarrow{F}}_1|=9$
$g=\sqrt{4k^2+4k^2+k^2}$
$9=3k$
$k=\mathrm{3...}\left(ii\right)$
$\text{putting (ii) in (i) we get}$
$\overrightarrow{W_1}=-12J$