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

Question

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, Straight line, Parabola, Circle, Ellipse

MARKS App · Accepted Answer

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.

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