Question

Four forces of 2N, 3N, 4N and 5N are acting on a body by making
angles of 0°, 90°,180° and 270° respectively. Find the magnitude and
direction of resultant force on the body?​

Answer 1

$\fcolorbox{black}{darkblue}{Question}$

Four forces of magnitudes 2N, 3N, 4N, and 5N are acting on a body at a point are inclined at 30°, 60°, 90°, and 120° respectively

$\fcolorbox{red}{pink}{Answer}$

$\fcolorbox{blue}{cyan}{text is here}$

$\fcolorbox{red}{pink}{Given, P1 =2N, P2 = 3N</p><p>}$

$\fcolorbox{blue}{cyan}{P3 = 4N and P4 = 5N</p><p></p><p>}$

$\fcolorbox{blue}{cyan}{These forces can be resolved into}$

$\fcolorbox{blue}{cyan}{components \: along \: the \:X \: and \: Y \: directions}$

$\fcolorbox{blue}{cyan}{ Rx =P1 \: cos \: theta1 +P2 \: cos \: theta2 +P2 \: cos3 +P4 \: cos \: theta4}$

$\fcolorbox{blue}{cyan}{ = 2cos30 + 3cos60 + 4coc90 + 5cos120}$

$2 \times \frac{ \sqrt{3} }{2} + 3 \times \frac{1}{2} + 4 \times 0 + 5 \frac{1}{2}$

$\fcolorbox{blue}{cyan}{ = 0.732 N}$

$\fcolorbox{blue}{cyan}{Ry =P1 \: sin \: theta1 +P2 \: sin \: theta2 + P3 \: sin \: theta3 +P4 \: sin \: theta4 }$

$\fcolorbox{blue}{cyan}{ = 2sin30 + 3sin60 +4sin90 + 5sin120}$

$= 2 \times \frac{1}{2} + 3 \times \frac{ \sqrt{3} }{2} + 4 \times 1 + 5 \times \frac{ \sqrt{3} }{2}$

$= 1 \times 1.5 \sqrt{3} + 4 +2.5 \sqrt{3}$

$\fcolorbox{blue}{cyan}{ = 1 + 2.59 + 4 + 4.33}$

$\fcolorbox{blue}{cyan}{ = 11.92 N}$

$\fcolorbox{blue}{cyan}{vo.7322 + 11.922}$

$\fcolorbox{blue}{cyan}{ = 11.96 N }$

$\fcolorbox{red}{pink}{mark \: as \: brainlist}$