A shell at rest at the origin explodes into three fragments of masses $1\ kg$ , $2\ kg$ and $m\ kg$ . The $1\ kg$ and $2\ kg$ pieces fly off with speeds of $5\ ms^{-1}$ along $x-axis$ and $6\ ms^{-1}$ along $y-axis$ respectively. If the $m\, kg$ piece flies off with a speed of $6.5\ ms^{-1}$ , the total mass of the shell must be    ......... $kg$

A shell, in flight, explodes into four unequal parts. Which of the following is conserved?

A bomb is projected with $200\,m/s$ at an angle $60^o$ with horizontal. At the highest  point, it explodes into three particles of equal masses. One goes vertically upward with  velocity $100\,m/sec$, second particle goes vertically downward with the same velocity as  the first. Then what is the velocity of the third one-

A lead ball strikes a wall and falls down, a tennis ball having the same mass and velocity strikes the wall and bounces back. Check the correct statement

A gun fires a bullet of mass $50 \,gm$ with a velocity of $30\,m\,{\sec ^{ - 1}}$. Because of this the gun is pushed back with a velocity of $1\,m\,{\sec ^{ - 1}}$. The mass of the gun is .......... $kg$

A shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/3$ remains stationary. The velocity of other part will be