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

Options

A. `30^(@)`
B. `60^(@)`
C. `90^(@)`
D. `120^(@)`

Answer

D

Explanation

`A= 3 N, B= 2 N then R = sqrt(A^(2)+B^(2)+2AB cos theta)`
`R=sqrt(9+4+12 cos theta)`….(i)
Now, `A= 6 N, B= 2` then
`2R =sqrt(36+4+24 cos theta)`….(ii)
from (i) and (ii) we get `cos theta= -1/2 :. theta= 120^(@)`