Question

At the initial moment three points $A,B$ and $C$ are on a horizontal straight line at equal distances from one another. Point $A$ begins to move vertically upward with constant velocity $v$ and point $C$ vertically downward without any initial velocity at constant acceleration $a$. Assuming the point begin to move simultaneously, then comment on the motion of the B such that centre of mass of the system doesn't move.

• A. acceleration $\frac{1}{2}a$ downwards and initial velocity $\frac{1}{2}v$ upwards
• B. retardation $\frac{1}{2}a$ and initial velocity $\frac{1}{2}v$ both upwards
• C. zero acceleration and initial velocity $v$
• D. acceleration $\frac{1}{2}a$ and initial velocity $\frac{1}{2}v$ both downwards

Answer 1

The correct option is A acceleration $\frac{1}{2}a$ downwards and initial velocity $\frac{1}{2}v$ upwards

For center of mass to be same, $y_{com}$ after moment is 0.

y-component of center of mass of A and C should be equal to y-component of B.

$y_B=\frac{-(vt-\frac{a{t}^2}{2})}{2}$

$y_B=-\frac{vt}{2}+\frac{a{t}^2}{4}$

acceleration $\frac{a}{2}$ downward and velocity $\frac{v}{2}$ upward.