Two particles of equal mass have velocities v → 1 = 4 i ^   ms − 1 and v → 2 = 4 j ^   ms − 1 . First particle has an acceleration a → 1 = 5 i ^ + 5 j ^   ms − 2 , while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

Step-by-step solution

Since, m 1 = m 2 = m v → cm = m 1 v → 1 + m 2 v → 2 m 1 + m 2 = m 2 m v → 1 + v → 2 = 1 2 × ( 4 i ^ + 4 j ^ ) = 2 ( i ^ + j ^ ) Similarly a → cm = m 1 a 1 → + m 2 a 2 → m 1 + m 2 = m 2 m ( a 1 → + a 2 → ) = 1 2 × ( 5 i ^ + 5 j ^ + 0 ) = 5 2 ( i ^ + j ^ ) Both v → c m and a → c m are parallel Centre of mass will move in a straight line because velocity and acceleration of centre of mass are in same direction.