A uniform chain of length $l$ and mass $m$ overhangs a smooth table with its two-thirds part lying on the table. Find the kinetic energy of the chain as it completely slips off the table.

In the figure, the stiffness of the spring is $k$ and the mass of the block is $m$. The pulley is fixed. Initially, the block $m$ is held such that the elongation in the spring is zero and then released from rest.

$\left(\mathrm{a}\right)$ Find the maximum elongation in the spring

$\left(\mathrm{b}\right)$ the maximum speed of the block $m$.

Neglect the mass of the spring and that of the string. Also, neglect the friction.

A spring-mass system $\left(m_1+\mathrm{massless} \mathrm{spring}+m_2\right)$ fall freely from a height $h$ before $m_2$ colliding inelastically with the ground. Find the maximum value of $h$ so that block $m_2$ will break off the surface. Assume $k=$ stiffness of the spring.