Question

Two particles of equal masses have velocities $\overrightarrow{V_1}=4\hat{i}m/s.$ and $\overrightarrow{V_2}=4\hat{j}m/s.$ The first particle has an acceleration $\overrightarrow{a_1}=(5\hat{i}+5\hat{j})\frac{m}{s^2}$, while the acceleration of the other particle is $zero.$ The center of mass of the particles moves in a :

• A. Circle
• B. Parabola
• C. Straight line
• D. Ellipse

Answer 1

Answer: (C)

Straight line

$X_{cm}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

$X_1=(4t+\frac{1}{2}5t^2)$

$X_1=0$

$X_{cm}=\frac{4t+\frac{1}{2}5t^2}{2}$

$Y_{cm}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}$

$y_1=\frac{1}{2}5t^2$

$y_2=4t$

$Y_{cm}=\frac{m(\frac{5}{2}+2)+m\left(4t\right)}{m+m}$

$Y_{cm}=\frac{4t+\frac{1}{2}5t^2}{2}$

$X_{cm}=y_{cm}$

center of mass moves in straight line

Answer C :