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

Options

A. `90^(@)`
B. `180^(@)`
C. `60^(@)`
D. `120^(@)`

Answer

D

Explanation

`R= sqrt((3P)^(2) + (2P)^(2) + 12P^(2) cos theta)`
`R= Psqrt(13 + 12 cos theta)`
`R_(1) = sqrt((6P)^(2) + (2P)^(2) + 23P^(2) cos theta)`
`=P sqrt(40 + 24 cos theta)`
`:. (R_(1))/(R ) = sqrt((40 + 24 cos theta)/(13 + 12 cos theta)) = 2`
or `40 + 24 cos theta = 52 + 48 cos theta`
or `24 cos theta = -12 " " theta = 120^(@)`