1.

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 :A. straight lineB. parabolaC. ellipseD. circle

Answer» Correct Answer - A
(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.


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