Question

Two small rings, each of mass 'm', are connected to the block of same mass 'm' through an inextensible massless string of length '$l$'. Rings are constrained to move over smooth rod AB. Initially, the system is held at rest as shown in Fig. Let $u$ and $\nu$ be the velocities of ring and block, respectively when string makes an angle ${60}^o$ with the vertical.

• A. $u=\sqrt{\frac{gl}{5}}$
• B. $u=\sqrt{\frac{8gl}{5}}$
• C. $\nu =\sqrt{3gl}$
• D. $\nu =\sqrt{\frac{3gl}{5}}$

Answer 1

Answer: (A), (D)

$\nu =\sqrt{\frac{3gl}{5}}$
$u=\sqrt{\frac{gl}{5}}$

$Given:$ Mass $=m$

length$=l$

$\theta ={60}^{\circ }$

$Solution:$

$v\cos \theta =u\sin \theta$

From conservation of energy

$mgl\cos \theta =2\left(\frac{1}{2}m{u}^2\right)+\frac{1}{2}m{v}^2$

$u=\sqrt{\frac{2gl\cos \theta }{2+{\tan }^2\theta }}=\sqrt{\frac{gl}{5}},\text{using}\theta ={60}^{\circ }$

$v=\sqrt{\frac{3gl}{5}}$

$So,the$ $correct$ $option:A,D$