Two identical bodies A and B of equal masses have initial velocities v₁ = 4 i m/s and v₂ = 4 j m/s respectively. The body A has acceleration a₁ = 6 i + 6 j m/s ^2 while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in __________ path.

Step-by-step solution

Velocity of the centre of mass is given by: v _ cm = m₁ v ₁ + m₂ v ₂ m₁ + m₂ Since m₁ = m₂ = m , we get: v _ cm = m(4 i ) + m(4 j ) 2m = 2 i + 2 j m/s Acceleration of the centre of mass is given by: a _ cm = m₁ a ₁ + m₂ a ₂ m₁ + m₂ a _ cm = m(6 i + 6 j ) + 0 2m = 3 i + 3 j m/s ^2 Here, v _ cm = 2( i + j ) and a _ cm = 3( i + j ) . Since the initial velocity and acceleration of the centre of mass are parallel to each other, the centre of mass moves in a straight line path. Answer: straight line