Rotational Motion Question 109
Question: The velocities of two particles $A$ and $B$ of same mass are $\vec{V}_A=a \vec{i}$ and $\vec{V}_B=b \hat{j}$ where $\mathrm{a}$ and $\mathrm{b}$ are constants. The acceleration of particle $A$ is $(2 a \hat{i}+4 b \hat{j})$ and acceleration of particle $B$ is $(a \hat{i}-4 b \hat{j})\left(\right.$ in $\left.m / s^2\right)$. The centre of mass of two particle will move in
Options:
A) straight line
B) parabola
C) ellipse
D) circle
Show Answer
Answer:
Correct Answer: A
Solution:
[a]
$ \vec{V} _{\text {com }}=\frac{m_1 \vec{V}_1+m_2 \vec{V}_2}{m_1+m_2}=\frac{\vec{V}_1+\vec{V}_2}{2}=\frac{a \hat{i}+b \hat{j}}{2} $
$ \vec{a} _{c o m}=\frac{a_1+a_2}{2}=\frac{3}{2}(a \hat{i}+b \hat{j}) $
$\vec{V} _{c o m} \text { is } $ parallel to $\vec{a} _{\text {com }}$.
Hence path will be a straight line.
