Question

A bomb of mass $9kg$ explodes into $2$ pieces of mass $3kg$ and $6kg$. The velocity of mass $3kg$ is $1.6m/s$, the K.E. (in $j$) of mass $6kg$ is

Answer 1

Find speed of the larger mass.
Given, mass of the bomb, $M=9kg$
Mass of the two pieces, $=3kg$ and $6kg$
Speed of the mass of $3kg=1.6m/s$
And initially the bomb is at rest. So initial momentum, $p_i=0$

As there is no external force act on the shell, so momentum will be conserved,
$0=3\times 1.6+6\times v$
$v=-0.8m/s$

$-ve$ sign indicates the opposite direction of the motion.

Find kinetic energy of the $6kg$ .
Formula used: $K.E=\frac{1}{2}m{v}^2$

Kinetic energy of the larger fragment,
$K.E=\frac{1}{2}m{v}^2$

$=\frac{1}{2}\times 6\times (0.8{)}^2=1.92j$