Consider a rocket is being fired. The kinetic energy of the rocket is increased by $16$ times where as its total mass is reduced by half through the burning of fuel. The factor by which its momentum increases is

The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to $8 \mathrm{s}$ is,

The figure shows the position - time $(x-t)$ graph of one-dimensional motion of a body of mass $0.4 \mathrm{kg}$. The magnitude of each impulse is

A constant force, $F=\frac{m_{1}g}{2}$ is applied on the block of mass $m_2$ as shown in figure. The string and the pulley are light and the surface of the table is smooth. Find the acceleration of $m_2$.