Question

A chain AB of mass m and length L is hanging on a smooth horizontal table as shown in figure. If it is released from the position shown, then displacement of centre of mass of chain in magnitude, when end A moves a distance $\frac{L}{2}$ is (L=32 m).

• A. $4\sqrt{2}$ m
• B. $8\sqrt{2}$ m
• C. $8$ m
• D. $4$ m

Answer 1

The correct option is B $8\sqrt{2}$ m

$m_1=\frac{\left(3m/4\right)\left(-32/8\right)+\left(m/4\right)\left(0\right)}{m}$

$=-9L/32=-9$

$n_2=\frac{\left(3m/4\right)\left(0\right)+\left(m/4\right)\left(-L/8\right)}{m}$

$=-L/32=-1$

$COM=\left(-9,t\right)$

$m_2=\frac{\left(m/4\right)\left(-2/8\right)+\left(3m/4\right)\left(0\right)}{m}$

$=-9L/32=-1$

$y_2=\frac{\left(m/4\right)\left(0\right)+\left(3m/4\right)\left(-32/8\right)}{m}$

$\left(-1,-a\right)=-2/32=-1$

So $\Rightarrow dBLau=8\sqrt{2}$.