In the arrangement shown, the pendulum on the left is pulled aside. It is then released and allowed to collide with other pendulums which is at rest. A perfectly inelastic collision occurs and the system rises to a height $\frac{h}{4}.$The ratio of the masses$\left(\frac{m_1}{m_2}\right)$of the pendulum is :

 

There are a hundred identical sliders equally spaced on a frictionless track as shown in the figure. Initially, all the sliders are at rest. Slider $1$ is pushed with velocity $v$ towards slider $2.$In a collision the sliders stick together. The final velocity of the set of hundred stuck sliders will be:

A particle of mass $m$ moves with velocity$v_0=20 \mathrm{m} {\sec }^{-1}$ towards a large wall that is moving with velocity $v=5 \mathrm{m} {\sec }^{-1}$ towards the particle as shown. If the particle collides with the wall elastically, the speed of the particle just after the collision is: