The velocities of two particles `A and B` of same mass are `vec V_A = a hat i` and `vec V_B = b hat j` where `a` and `b` are constants. The acceleration of particle A is `(2 a hat i+ 4 b hat j)` and acceleration of particle B is `(a hat i- 4 b hat j)` in `(m//s^2)`. The centre of mass of two particle will move in :

Options

A. straight line
B. parabola
C. ellipse
D. circle

Answer

A

Explanation

(a) `vec V_(com) = (m_1 vec V_1 + m_2 vec V_2)/(m_1 + m_2) = (vec V_1 + vec V_2)/(2) =(a hat i + b hat j)/(2)`
`vec a_(com) = (a_1 + a_2)/(2) =(3)/(2) (a hat i + b hat j)`
`vec V` is parallel to `vec a_(com)`. Hence path will be a straight line.