Two forces of equal magnitude (F) act at an angle of β to each other. The resultant of these forces will be given by:

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  1. 2F
  2. 2F × cos β
  3. 2F × cos (β/2)  
  4. F × cos (β/2)

Answer (Detailed Solution Below)

Option 3 : 2F × cos (β/2)  

Detailed Solution

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Concept:

F1 Ashik Madhu 14.08.20 D8

If two forces of equal magnitude (F) act at an angle of β to each other, then the resultant of these forces is given by

\({\bf{R}} = \sqrt {{{\bf{F}}^2} + {{\bf{F}}^2} + 2 \times {\bf{F}} \times {\bf{F}} \times {\bf{cosβ }}} \)

\( R= \sqrt {2{{\rm{F}}^2} + (2{{\rm{F}}^2} \times {\rm{cosβ )}}} \)

\(R = \sqrt {2{F^2}(1 + \cos \beta )} \)       

 \(\therefore {\bf{R}} = 2{\bf{Fcos}}\left( {\frac{{\bf{β }}}{2}} \right)\)      \(\left( \because{1 + {\rm{cosβ }} = 2\cos^2 \left( {\frac{{\rm{β }}}{2}} \right)} \right)\)

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