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Resultant of two froce 3N nad 4N acting ar apoit is 5N show that the two froce are 2 perpendicular to each other​

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  • Two forces – A = 3N and B = 4N
  • Resultant of these forces, R = 5N

[tex]\qquad[/tex] ☀️We are asked to prove that two forces are perpendicular to each other.

  • Formula to calculate magnitude of resultant 'R' of two forces 'A' and 'B' when they are at an angle 'p' to each other.

[tex]\qquad[/tex][tex]\purple{ \longrightarrow \bf R^2= A^2 + B^2 + 2 AB cos p} [/tex]

[tex]\qquad[/tex][tex] \longrightarrow \sf 5^2= 3^2 + 4^2+ 2 \times 3\times 4\times cos p[/tex]

[tex]\qquad[/tex][tex] \longrightarrow \sf 25 = 9 + 16 + 24 cos p [/tex]

[tex]\qquad[/tex][tex] \longrightarrow \sf 25 = 25 + 24 cos p[/tex]

[tex]\qquad[/tex][tex] \longrightarrow \sf 25 - 25 = 24 cos p[/tex]

[tex]\qquad[/tex][tex] \longrightarrow \sf 0 = 24 cos p[/tex]

[tex]\qquad[/tex][tex] \longrightarrow \sf cos p = 0[/tex]

[tex]\qquad[/tex][tex] \longrightarrow \sf cos p = cos 90°[/tex]

[tex]\qquad[/tex][tex]\purple{ \longrightarrow \sf p = 90°}[/tex]

Hence, Proved that –

  • Forces A = 3N and B = 4N are Perpendicular to each other.

[tex]\qquad[/tex]_________________________

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