Question

The forces acting on the blocks are shown. What is the displacement of centre of mass in time t? The initial velocity of each is zero.

• A. $\frac{F_o{t}^2}{6m}$
• B. $\frac{F_o{t}^2}{2m}$
• C. $\frac{F_o{t}^2}{3m}$
• D. $\frac{F_o{t}^2}{6m}$

Answer 1

The correct option is D

$\frac{F_o{t}^2}{6m}$

${\overrightarrow{a}}_{cm}=\frac{{\overrightarrow{F}}_{net}}{M_{Total}\Rightarrow {\overrightarrow{a}}_{cm}}=\frac{2{\overrightarrow{F}}_o-{\overrightarrow{F}}_o}{3m}=\frac{{\overrightarrow{F}}_o}{3m}$

initial Velocity of each block is zero.

So initial velocity of centre of mass, $U_{c}m$ = 0

$\therefore$Displacement of centre of mass in time 't' ,

$S_{cm}=u_{cm}t+\frac{1}{2}{s}_{cm}{t}^2$

$S_{cm}=\frac{1}{2}{s}_{cm}{t}^2$

$\Rightarrow S_{cm}=\frac{1}{2}\left(\frac{F_o}{3m}\right)t^2=\frac{F_o{t}^2}{6m}$