Question

Two particles of equal mass have velocities $\overrightarrow{{\upsilon }_1}=4\hat{i}m{s}^{-1}$ and $\overrightarrow{{\upsilon }_2}=4\hat{j}m{s}^{-1}$. First particles has an acceleration ${\vec{a}}_1=\left(5\hat{i}+5\hat{j}\right)m{s}^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

• A. straight line
• B. parabola
• C. circle
• D. ellipse

Answer 1

Answer: (A)

$<br/>\begin{array}{l}<br/>X_{cm}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}\\ <br/>X_1=\left(4t+\frac{1}{2}5t^2\right)\\ <br/>X_2=0\\ <br/>X_{cm}=\frac{4t+\frac{1}{2}5t^2}{2}\\ <br/>Y_{cm}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}\\ <br/>y_1=\frac{1}{2}5t^2\\ <br/>y_2=4t\\ <br/>Y_{cm}=\frac{m\left(\frac{5}{2}+2\right)+m(4t)}{m+m}\\ <br/>Y_{cm}=\frac{4t+\frac{1}{2}5t^2}{2}\\ <br/>X_{cm}=Y_{cm}<br/>\end{array}<br/>$
Hence centre of mass moves in a straight line