Question

The magnitude of resultant of two forces of magnitudes 3P and 2P is R. If the first force is doubled, the magnitude of the resultant is also doubled. The angle between the two forces is :

Answer 1

Answer:

Explanation:

Hope it helps

Answer 2

Answer:

Angle between the forces is 120°.

Explanation:

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°.