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. (a) circular (b) parabolic (c) straight line (d) elliptical

Answer: (c). Equal masses: vcm = (4i + 4j)/(2) = 2i + 2j m/s. acm = ((6i+6j) + 0)/(2) = 3i + 3j m/s ². acm is constant and parallel to vcm, so the CM only speeds up along the same line. So the answer is (c) straight line.

Two identical bodies A and B of equal masses have initial velocities… | JEE Main 2026 (6 Apr, Shift 2)

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Motion of Centre of Mass

Two identical bodies A and B of equal masses have initial velocities $\overrightarrow{v_1} = 4\hat{i}\text{ m/s}$ and $\overrightarrow{v_2} = 4\hat{j}\text{ m/s}$ respectively. The body A has acceleration $\overrightarrow{a_1} = 6\hat{i} + 6\hat{j}\text{ m/s}^2$ while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in ______ path.

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Answer: (c)

Equal masses: $\vec{v}_{cm} = \frac{4\hat{i} + 4\hat{j}}{2} = 2\hat{i} + 2\hat{j}$ m/s.
$\vec{a}_{cm} = \frac{(6\hat{i}+6\hat{j}) + 0}{2} = 3\hat{i} + 3\hat{j}$ m/s $^2$ .
$\vec{a}_{cm}$ is constant and parallel to $\vec{v}_{cm}$ , so the CM only speeds up along the same line.
So the answer is (c) straight line.

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