Question

The system in figure is released from rest from the position shown. After, blocks have moved a distance $H/3$, collar B is removed and block A and C continue to move. What is the speed of C just before it strikes the ground. There is no friction anywhere. Neglect any impulse on string when B is stopped. Neglect size of collar and blocks (Given acceleration due to gravity $=g$).

• A. $\sqrt{\frac{13gH}{9}}$
• B. $\frac{4}{3}\sqrt{gH}$
• C. $2\sqrt{\frac{gH}{3}}$
• D. $\sqrt{\frac{10gH}{3}}$

Answer 1

Answer: (A)

$\sqrt{\frac{13gH}{9}}$

acceleration of system before removing collar $2mg/3m=2g/3$

acceleration after removing collar $=mg/2m=g/2$

speed of c just before removing collar $v_1=\sqrt{0^2+2\times a\times s}=\sqrt{2\times \frac{2g}{3}\times \frac{H}{3}}=\frac{2}{3}\sqrt{gH}$

speed of c just before hitting the ground $v_2=\sqrt{(\frac{2}{3}\sqrt{gH}{)}^2+2\times \frac{g}{2}\times H}=\sqrt{\frac{13gH}{9}}$