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Question

Two particles of equal mass have initial velocities 2^ims1and2^jms1. First particle has a constant acceleration (^i+^j)ms1 while the acceleration of the second particle is always zero. The centre of mass of the two particles moves in :

A
Circle
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B
Parabola
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C
Ellipse
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D
Straight line
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Solution

The correct option is D Straight line
Velocity of center of mass is given by:
v=v1m1+v2m2m1+m2=i+j
Acceleration of center of mass is given by:
a=a1m1+a2m2m1+m2=12(i+j)
Acceleration and velocity both have the same direction, hence the body moves along the same line (i+j).
Hence it moves in a straight line.
Option D is correct.

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