$A$ body of mass $m$ moving with velocity $v$ undergoes a head-on elastic collision with another body of mass $2m$ which is initially at rest. The ratio of the kinetic energy $(K.E.)$ of the colliding body before and after the collision is: (in $: 1$)

$A$ block of mass $m$ slides with speed $v$ on a frictionless table towards another stationary block of mass $m$. $A$ massless spring with spring constant $k$ is attached to the second block as shown in the figure. The maximum distance the spring gets compressed is

Three blocks are initially placed as shown in the figure. Block $A$ has mass $m$ and initial velocity $v$ to the right. Block $B$ with mass $m$ and block $C$ with mass $4m$ are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of block $A$ is

$A$ heavy body moving with a velocity of $6\,ms^{-1}$ collides elastically with a light body (whose mass is half of the mass of the heavy body) at rest. The velocity of the light body will be (in $ms^{-1}$):

$Assertion$ : In an elastic collision of two billiard balls,the total kinetic energy is conserved during the short time of oscillation of the balls (i.e.,when they are in contact).
$Reason$ : Energy spent against friction does not follow the law of conservation of energy.

$A$ neutron moving with velocity $u$ collides elastically with an atom of mass number $A$. If the collision is head-on and the initial kinetic energy of the neutron is $E$, then the final kinetic energy of the neutron after the collision is: