Two identical bodies A and B of equal masses have initial velocities $\vec{v}_1=4 \hat{i} \mathrm{~m} / \mathrm{s}$ and $\overrightarrow{v_2}=4 \hat{j} \mathrm{~m} / \mathrm{s}$ respectively. The body A has acceleration $\overrightarrow{a_1}=6 \hat{i}+6 \hat{j} \mathrm{~m} / \mathrm{s}^2$ while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in $\_\_\_\_$ path.
Select the correct option:
A
circular
B
parabolic
C
straight line
D
elliptical
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$$
\begin{aligned}
& \vec{v}_{c m}=\frac{m_1 \vec{v}_1+m_2 \vec{v}_2}{m_1+m_2}=\frac{m(4 \hat{i})+m(4 \hat{j})}{2 m}=2 \hat{i}+2 \hat{j} \\
& \vec{a}_{\mathrm{cm}}=\frac{\mathrm{m}_1 \overrightarrow{\mathrm{a}}_1+\mathrm{m}_2 \overrightarrow{\mathrm{a}}_2}{\mathrm{~m}_1+\mathrm{m}_2}=\frac{\mathrm{m}(6 \hat{\mathrm{i}}+6 \hat{\mathrm{j}})+\mathrm{m}(0)}{2 \mathrm{~m}}=3 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}
\end{aligned}
$$
$\overrightarrow{\mathrm{V}}_{\mathrm{cm}}$ and $\overrightarrow{\mathrm{a}}_{\mathrm{cm}}$ are parallel
so, path is straight line
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