Question

The figure shows mass m moves with velocity u. Find the velocity of ring at that moment. Ring is restricted to move on smooth rod.

Answer 1

Given:

The figure shows mass m moves with velocity u.

To find:

Velocity of ring at that moment.

Calculation:

This question is based on Constraint Phenomenon.

Velocity component of the ring along the wire will have to be same as that of the velocity of mass m such that constraint is maintained.

Let Velocity of Ring be v ;

$\therefore \: \rm{v \cos( {60}^{ \circ} ) = u}$

$\rm{ = > \: v = \dfrac{u}{ \cos( {60}^{ \circ} ) } }$

$\rm{ = > \: v = \dfrac{u}{( \frac{1}{2} )} }$

$\rm{ = > \: v = 2u}$

So, final answer is:

$\boxed{ \bf{ \huge{ \: v = 2u}}}$