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

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Conservation of Momentum

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✓ Correct
(D)elliptical

Answer: (C)

Solution

The centre of mass velocity is

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

, and its acceleration is

a_{c m} = \frac{a _{1} + 0}{2} = 3 \hat{i} + 3 \hat{j}

. Both vectors point along

\hat{i} + \hat{j}

, so the velocity and acceleration of the centre of mass are parallel and it moves along a straight line.

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Single correct option

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