A balloon has a mass of $10$ gram in air. The air escapes from the balloon at a uniform rate with a velocity of $5 \mathrm{cm} {\mathrm{s}}^{-1}$ and the balloon shrinks completely in $2.5 \mathrm{s}$. The average force acting on the balloon will be

Figure represents the position-time graph of a body of mass $4 \mathrm{kg}$. Impulse $\left(\mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}\right)$ imparted to the body at $t=0$ is

Figure shows a rectangular copper plate with its centre of mass at the origin $O$ and side $AB=2BC=2 \mathrm{m}.$ If a quarter part of the plate (shown as shaded) is removed, the centre of mass of the remaining plate would lie at

Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2v$ respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at $A$, these two particles will again reach the point $A$?