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(d) 19The resultant of two forces 3P and 2P is R. Ifthe first force is doubled then the resultantforce is(a) 120°isfarg doubled. The angle bebwunesi the 999(b) 60(d) 90°(c) 180

Answer»

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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