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 magni

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1. 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.

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2. Explanation:

   [tex]\huge\orange{\mid{\fbox{\tt{Question ⇛}}\mid}}[/tex]

   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.

   [tex]\huge\blue{\mid{\fbox{\tt{Answer ⇛}}\mid}}[/tex]

   [tex]\huge\mathfrak\red{Solution☟}[/tex]

   [tex]Let \: A \: and \: B \: be \: the \: two \: forces. [/tex]

   [tex]Then \: A=3x, \: B=5x; \: R=28N \: and \: θ= \: 60°. [/tex]

   [tex]Dividing \: A \: by \: B , \: \frac{A}{B} = \frac{3}{5} [/tex]

   [tex]We \: know \: that \: R \: = \sqrt{ a {}^{2} +B {}^{2} +2AB \: cosθ}[/tex]

   [tex]⇒28 \: = \: \sqrt{ (3x) {}^{2} +(5x) {}^{2} +2(3x)(5x)cos60°}[/tex]

   [tex]⇒ \sqrt{ 9x {}^{2} +25x {}^{2} +15x {}^{2}} =7x[/tex]

   [tex]⇒x= \frac{28}{7} =4[/tex]

   ⇝[tex]Hence, \: forces \: are A=3×4=12N,B=5×4=20N[/tex]

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