A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to:

A body of mass  $M$  is dropped from a height  $h$  on a sand floor. If the body penetrates $x\,\,cm$  into the sand, the average resistance offered by the sand of the body is

$A$ ball is dropped from $a$ height $h$. As it bounces off the floor, its speed is $80$ percent of what it was just before it hit the floor. The ball will then rise to $a$ height of most nearly .............. $\mathrm{h}$

$Assertion$ : If collision occurs between two elastic bodies their kinetic energy decreases during the time of collision.
$Reason$ : During collision intermolecular space decreases and hence elastic potential energy increases

A bullet of mass $m$ moving with a speed $v$ strikes a wooden block of mass $M$ and gets embedded into the block. The final speed is

A body of mass $m= 10^{-2} \;kg$ is moving in a medium and experiences a frictional force $F= -kv^2$ Its intial speed is $v_0= 10$ $ms^{-1}$ If, after $10\ s$, its energy is $\frac{1}{8}$ $mv_0^2$ the value of $k$ will be