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The resultant of two forces 3p and 2p is R.If the first force is doubled then the resultant is also doubled.then the angle between is the two forces us?

The resultant of two forces 3p and 2p is R.If the first force is doubled then the resultant is also doubled.then the angle between is the two forces us?

Grade:11

1 Answers

Khimraj
3007 Points
4 years ago
Resultant,R =√(a^2+b^2+2abcosx)
As, r = √{(3p)^2+(2p)^2+2×3p×2p×cosx}
or, r = √(9p^2+4p^2+12p^2cosx)
or, r = √(13p^2+12p^2cosx)
According to question;
2r = √{(6p)^2+(2p)^2+2×6p×2p×cosx}
or, 2r =√(36p^2+4p^2+24p^2cosx)
or, 2r = √(40p^2+24p^2cosx)
or, 2{√(13p^2+12p^2cosx)} 
= √(40p^2+24p^2cosx)
or, 4(13p^2+12p^2cosx) = (40p^2+24p^2cosx)
or, 52p^2 + 48p^2cosx= 40p^2 + 24p^2cosx
or, 12 p^2 = - 24 p^2cosx
or, cosx = - 1/2 
or, x = cos^-1(-1/2)
or, x = 120°
So, angle between the forces is 120°.

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