An object of mass $3\,m$ splits into three equal fragments. Two fragments have velocities $v\hat j$ and $v\hat i$. The velocity of the third fragment is

A bomb of $12\, kg$ explodes into two pieces of masses $4\, kg$ and $8\, kg$. The velocity of $8\, kg$ mass is $6\, m/sec$. The kinetic energy of the other mass is .............. $\mathrm{J}$

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

A stationary body of mass $m$ gets exploded in $3$ parts having mass in the ratio of $1 : 3 : 3$. Its two fractions having equal mass moving at right angle to each other with velocity of $15\,m/sec$. Then the velocity of the third body is

A cannon ball is fired with a velocity $200\, m/sec$ at an angle of $60^o$ with the horizontal. At the highest point of its flight it explodes into $3$ equal fragments, one going vertically upwards with a velocity $100\, m/sec$, the second one falling vertically downwards with a velocity $100\, m/sec$. The third fragment will be moving with a velocity

A shell of mass $m$ moving with velocity $ v$ suddenly breaks into $2$ pieces. The part having mass $m/4$ remains stationary. The velocity of the other shell will be