The square of resultant of two equal forces is three times their product. Angle between the force is

Options

A. `pi`
B. `(pi)/2`
C. `(pi)/4`
D. `(pi)/3`

Answer

D

Explanation

Let `theta` be the angle between two vectors `P` and `Q` whose resultant is `R`.
here `P=Q`
and `R^(2)=3PQ=3P^(2)`
As `R^(2)=P^(2)+Q^(2)+2PQcos theta`
`:.3P^(2)=P^(2)+P^(2)+2P^(2)cos theta`
Taking square on both sides
`implies3P^(2)-2P^(2)=2P^(2)cos theta`
`implies P^(2)=2P^(2)cos theta`
`implies1=2cos theta`
`:.cos theta=1//2`, thus
`cos theta =cos 60^(@)`
or `theta=60^(@)=pi//3`