A sphere of mass $0.1\,\,kg$  is attached to a cord of $1\,m$ length. Starting from the height of its point of suspension this sphere hits a block of same mass at rest on a frictionless table. If the impact is elastic, then the kinetic energy of the block after the collision is ............. $\mathrm{J}$

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

A vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is

A bomb of mass $9\, kg$ explodes into two pieces of masses $3\, kg$ and $6\, kg$. The velocity of mass $3\, kg$ is $16\, m/s$. The $KE$ of mass $6\, kg$ (in joule) is

A uniform chain of length $2\,m$ is kept on a table such that a length of $60\,\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table .............. $\mathrm{J}$

Four particles $A, B, C$ and $D$ of equal mass are placed at four corners of a square.  They move with equal uniform speed $v$ towards the intersection of  the diagonals. After  collision, $A$ comes to rest, $B$ traces its path back with same speed and $C$ and $D$ move with equal speeds. What is the velocity of $C$ after collision