JEE Main 2026 Apr 6 Shift 2, Physics Q7: Centre of Mass

JEE Main2026Apr 6, Shift 2Physics

Two identical bodies A and B of equal masses have initial velocities $v_{1} = 4 \hat{i}$ m/s and $v_{2} = 4 \hat{j}$ m/s respectively. The body A has acceleration $a_{1} = 6 \hat{i} + 6 \hat{j}$ m/s $^{2}$ while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in _____ path.

A
circular
B
parabolic
C
straight line
D
elliptical

Solution

Compute the centre-of-mass velocity and acceleration (equal masses):

$v_{c m} = \frac{m v _{1} + m v _{2}}{2 m} = \frac{4 i ^ + 4 j ^}{2} = 2 \hat{i} + 2 \hat{j}$

$a_{c m} = \frac{m a _{1} + m ( 0 )}{2 m} = \frac{6 i ^ + 6 j ^}{2} = 3 \hat{i} + 3 \hat{j}$

$v_{c m}$ and $a_{c m}$ are parallel (both along $\hat{i} + \hat{j}$ ), so the centre of mass moves along a straight line.

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JEE Main 2026 Apr 6 Shift 2, Physics Q7: Centre of Mass

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