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Grade 11Mechanics

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?

Deepak Kumar Yadav

7 Years agoGrade 11

1 Answer

Khimraj

7 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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