A bullet of mass $200\,g$ having initial kinetic energy $90\,J$ is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to $40\,J$ within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is $.....m$

$A$ force exerts an impulse $I$ on a particle changing its speed from $u$ to $2u$. The applied force and the initial velocity are oppositely directed along the same line. The work done by the force is

$STATEMENT$-$1$ A block of mass $\mathrm{m}$ starts moving on a rough horizontal surface with a velocity $\mathrm{v}$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of $30^{\circ}$ with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. because

$STATEMENT$- $2$ The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

A chain is on a frictionless table with one fifth of its length hanging over the edge. If the chain has length $L$ and mass $M$, the work required to be done to pull the hanging part back onto the table is

A block of mass $2\, kg$ is placed on a rough inclined plane as shown in the figure $(\mu = 0.2)$ so that it just touches the spring. The block is allowed to move downwards. The  spring will be compressed to a maximum of .............. $\mathrm{cm}$

A $2\ kg$ object is floating at rest, acted upon by only force as indicated in figure. Find the total work done by the force in $3\ sec$ ..................... $\mathrm{J}$