Question

Two forces whose magnitudes are in the ratio 3:5 give a resultant of 28N. If the angle of their inclination is 60°, find the magnitude of each force. ​

Answer 1

Explanation:

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Two forces whose magnitudes are in the ratio 3:5 give a resultant of 28N. If the angle of their inclination is 60°, find the magnitude of each force. 

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$\huge\mathfrak\red{Solution☟}$

$Let  \: A  \: and  \: B  \: be \: the \: two \: forces.$

$Then  \: A=3x, \: B=5x; \: R=28N  \: and \:  θ= \: 60°.$

$Dividing  \: A \:  by \: B ,  \: \frac{A}{B} = \frac{3}{5}$

$We \: know \: that \:  R \: = \sqrt{ a {}^{2} +B {}^{2} +2AB \: cosθ}$

$⇒28 \: = \: \sqrt{ (3x) {}^{2} +(5x) {}^{2} +2(3x)(5x)cos60°}$

$⇒ \sqrt{ 9x {}^{2} +25x {}^{2} +15x {}^{2}} =7x$

$⇒x= \frac{28}{7} =4$

⇝$Hence, \: forces \: are  A=3×4=12N,B=5×4=20N$

Answer 2

Explanation:

Two forces whose magnitudes are in the ratio 3:5 give a resultant of 28N. If the angle of their inclination is 60°, find the magnitude of each force.