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Maths-

General

Easy

Question

If the resultant of two forces is equal in magnitude to one of the components and perpendicular to it in direction, find the other component using the vector method

$135^{\circ}$
$120^{\circ}$
$90^{\circ}$
$45^{\circ}$

The correct answer is: $135 to the power of ring operator end exponent$

Let P be horizontal in the direction of unit vector $i$ The resultant is also P but perpendicular to it in the direction of unit vector $j$ If Q be the other force making an anlgeq (obtuse ) as resultnat is perpendicular to P , then the two forces are P $i$ and Q $c o s invisible function application theta stack i with hat on top to the power of plus Q end exponent s i n invisible function application theta stack j with hat on top text resultant is end text P stack j with hat on top$
$therefore stack P with hat on top equals stack P i plus with hat on top open parentheses Qcos invisible function application theta stack i with hat on top plus Qsin invisible function application theta stack j with hat on top close parentheses$
comparing coefficients of $stack i with hat on top$ and $j$ we get
$table row cell P plus Q c o s invisible function application theta equals 0 text end text text a end text text n end text text d end text text end text Q s i n invisible function application theta equals P end cell row cell text end text text o end text text r end text text end text Q c o s invisible function application theta equals negative P text end text text a end text text n end text text d end text text end text Q s i n invisible function application theta equals P end cell row cell text end text text S end text text q end text text u end text text a end text text r end text text i end text text n end text text g end text text end text text a end text text n end text text d end text text end text text a end text text d end text text d end text text i end text text n end text text g end text text end text Q equals P square root of 2 text end text text a end text text n end text text d end text text end text text d end text text i end text text v end text text i end text text d end text text i end text text n end text text g end text text end text end cell row cell t a n invisible function application theta equals negative 1 end cell row cell theta equals 135 to the power of ring operator end exponent end cell end table$

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