Two particles of equal mass have velocities v → 1 = 4 i ^   ms − 1 and v → 2 = 4 j…

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

Solution

Since, m 1 = m 2 =m

v → cm = m 1 v → 1 + m 2 v → 2 m 1 + m 2 = m 2m 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 2m ( a 1 → + a 2 → )

= 1 2 ×(5 i ^ +5 j ^ +0)

= 5 2 ( i ^ + j ^ )

Both v → cm and a → cm are parallel

Centre of mass will move in a straight line because velocity and acceleration of centre of mass are in same direction.

Asked in: Practice

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