Two identical bodies A and B of equal masses have initial velocities v_1 = 4 i m/s and v_2 = 4 j m/s respectively. The body A has acceleration a_1 =…
JEE Main 2026 — Physics Mechanics
2026mcqmedium
Two identical bodies A and B of equal masses have initial velocities v1=4i^ m/s and v2=4j^ m/s respectively. The body A has acceleration a1=6i^+6j^ m/s2 while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in __________ path.
Official previous-year question
Held on 6 Apr 2026 · Verified 6 Jul 2026.
Options
A
circular
B
parabolic
C
straight line
D
elliptical
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Solution
Velocity of the centre of mass is given by:
vcm=m1+m2m1v1+m2v2
Since m1=m2=m, we get:
vcm=2mm(4i^)+m(4j^)=2i^+2j^ m/s
Acceleration of the centre of mass is given by:
acm=m1+m2m1a1+m2a2
acm=2mm(6i^+6j^)+0=3i^+3j^ m/s2
Here, vcm=2(i^+j^) and acm=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
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