Question

The system in figure is released from rest from the position shown. After blocks have moved distance H/3, collar B is removed and block A and C continue to move. The speed of C just before it strikes the ground is

• A. $\frac{4}{3}\sqrt{gH}$
• B. $2\frac{\sqrt{gH}}{3}$
• C. $\frac{\sqrt{13gH}}{3}$
• D. $2\sqrt{2gH}$

Answer 1

Answer: (C)

$\frac{\sqrt{13gH}}{3}$

initially:$2mg-T_1=2m{a}_1$

$T_1=m{a}_1$

$a_1=\frac{2g}{3}$

$V_1=$ velocity of block e after $\frac{H}{3}$ $V_1=\sqrt{2\times \frac{2g}{3}\times \frac{H}{3}}$

$V_1=\frac{2}{2}\sqrt{gH}$

$V_2=$ velocity of block

e after just striking $V_2=V_1^2+2a_{2}S$

where $S=H$

and $a_2=g/2$

$V_2=\frac{1}{3}\sqrt{13gH}$

Correct option is (C).