A system consists of three masses $m_1, m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_1$ hangs freely $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction = $\mathrm{\mu }$). The pulley is frictionless and is of negligible mass. The downward acceleration of mass $m_1$ is: (Assume $m_1=m_2=m_3=m$). 

Three blocks $A, B$ and $C$ of masses $4 \mathrm{kg}, 2 \mathrm{kg}$ and $1 \mathrm{kg}$ respectively, are in contact on a frictionless surface, as shown. If a force of $14 \mathrm{N}$ is applied on the $4 \mathrm{kg}$ block, then the contact force between $A$ and $B$ is:

A sphere of radius $25 \mathrm{cm}$ and mass $1 \mathrm{kg}$ is hung by a string of negligible mass and length $40 \mathrm{cm}$, then tension in the string is:-

Find the tension in the string if $\mathrm{\theta }$$=30°$ and the mass hung in the middle of the string is equal to $22 \mathrm{kg}$.

A rigid ball of mass m strikes a rigid wall at $60°$ and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be:- 
 

In the following diagram find value of $T_2$.