Two identical bodies A and B of equal masses have initial velocities and respectively. The body A has acceleration

Question

Two identical bodies A and B of equal masses have initial velocities ${\vec{v}}_{1} = 4 \hat{i} m / s$ and ${\vec{v}}_{2} = 4 \hat{j} m / s$ respectively. The body A has acceleration ${\vec{a}}_{1} = 6 \hat{i} + 6 \hat{j} m / s^{2}$ while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in ______ path. [2026]

Smart Achievers · Accepted Answer

(3)

${\vec{v}}_{cm} = \frac{m_{1} {\vec{v}}_{1} + m_{2} {\vec{v}}_{2}}{m_{1} + m_{2}} = \frac{m (4 \hat{i}) + m (4 \hat{j})}{2 m} = (2 \hat{i} + 2 \hat{j}) m / s$

${\vec{a}}_{cm} = \frac{m_{1} {\vec{a}}_{1} + m_{2} {\vec{a}}_{2}}{m_{1} + m_{2}} = \frac{m (6 \hat{i} + 6 \hat{j}) + m (0)}{2 m} = 3 \hat{i} + 3 \hat{j}$

${\vec{v}}_{cm} and {\vec{a}}_{cm} are along same line so path is a straight line.$

Solution

1 circular

2 parabolic

3 straight line

4 elliptical

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