Centre of Mass, Momentum and Collision

A block of mass 2 kg is attached with a spring of spring constant $$4000$$ Nm$$^{-1}$$ and the system is kept on smooth horizontal table. The other end of the spring is attached with a wall. Initially spring is stretched by 5 cm from its natural position and the block is at rest. Now suddenly an impulse of $$4$$ kg-ms$$^{-1}$$ is given to the block towards the wall.
A thin rod of length $$ \ell$$ and mass m is suspended horizontally by two vertical strings, A & B, one attached at each end of the rod. The density of the rod is given by $$\rho (x)=$$$${{\rho _ 0}(x/\ell )^ 3}$$ where x = 0 corresponds to the position of string A. Give your answer in terms of m, $$\ell $$ and g.
Two particles, each of mass $$m$$, are connected by a light inextensible string of length $$2l$$. Initially they lie on a smooth horizontal table at points $$A$$ and $$B$$ distance $$l$$ apart. the particle at $$A$$ is projected across the table with velocity $$u$$. Calculate (in terms of $$m$$ and $$u$$) the impulse of tension in the string.
Particle 1 experiences a perfectly elastic collision with a stationary particle 2.
A molecule collides with another, stationary, molecule of the same mass.