In a system of particles $8 \mathrm{kg}$ mass is subjected to a force of $16 \mathrm{N}$ along $+$ ve $x$ -axis and another $8 \mathrm{kg}$ mass is subjected to a force of $8 \mathrm{N}$ along $+$ ve $y$ -axis. The magnitude of acceleration of centre of mass and the angle made by it with $x$ -axis are given, respectively, by 
 

Two blocks $m_1$ and $m_2$ are pulled on a smooth horizontal surface, and are joined together with a spring of stiffness $k$ as shown in figure. Suddenly, block $m_2$ receives a horizontal velocity $v_0$, then the maximum extension $x_m$ in the spring is

An object of mass $10 \mathrm{kg}$ is launched from the ground at $t=0,$ at an angle of $37°$ above the horizontal with a speed of $30 \mathrm{m}/\mathrm{s}.$ At some time after its launch, an explosion splits the projectile into two pieces. One piece of mass $4 \mathrm{kg}$ is observed at $(105 \mathrm{m}, 43 \mathrm{m})$ at $t=2 \mathrm{s}.$ Find the location of second piece at $t=2 \mathrm{s}.$

For the system shown in figure, the string is light and pulley is frictionless. The $4 \mathrm{kg}$ block is given an upward velocity of $1 \mathrm{m}/\mathrm{s}$ The centre of mass of the two blocks
will [neglect the impulse duration]