# Why is the kinetic energy of this particle of mass $m$ zero at the bottom point? [closed]

Why is the final kinetic energy of the particle of mass m zero.It should have some velocity when it reaches the bottom??

Can we solve this solve by using the concept of reduced mass system?

• Typeset mathematical terms using MathJax rather than posting image of question. Here's the tutorial. – SarGe Jul 8 at 5:25

Because we need the minimum speed by which the circle gets completed i.e. it stops when the circle is just completed. If the speed given to $$m$$ is greater than $$\displaystyle \sqrt{\frac{4gl}{3}}$$ then it completes the circle as well as have some velocity at the lowest point.
The torque of mass $$2m$$ is greater than that of $$m$$ about the center of rod and hence it will tend to rotate the rod on clockwise direction (if velocity given to $$m$$ is towards left). But, if $$m$$ has sufficient angular momentum, then it can it can complete the circle. However, the torque due to $$2m$$ will oppose this motion, too.
Also, for a system of two particles with masses $$m_1$$ and $$m_2$$ exerting equal and opposite forces on each other and subject to no external forces, concept of reduced mass can be used which is not the case here.
• No, both will be at rest for $v_{min}$. – SarGe Jul 8 at 5:50