Two blocks $A$ and $B$ of masses $1\, kg$ and $2\, kg$ are connected together by a  spring and are resting on a horizontal surface. The blocks are pulled apart so as to strech  the spring and then released. The ratio of $K.E.s$ of both the blocks is

A neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is

In the non-relativistic regime, if the momentum, is increased by $100\%$, the percentage increase in kinetic energy is

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

$ABCDE$ is a channel in the vertical plane, part $BCDE$ being circular with radius $r$ . A block is released from $A$ and slides without friction and without rolling. The block will complete the loop if $h$ is

A body moving with speed $v$ in space explodes into two piece of masses in the ratio $1 : 3.$ If the smaller piece comes to rest, the speed of the other piece is