d
\(\begin{array}{l}
\,\,\,\,When\,an\,{\rm{explosion}}\,breaks\,a\,rock,\\
by\,the\,law\,of\,conservation\,of\,momentum,\,\\
initial\,momentum\,is\,zero\,and\,for\,the\\
three\,pieces,\\
Total\,momentum\,of\,the\,two\,pieces\,\\
1\,kg\,and\,2\,kg\,\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt {{{12}^2} + {{16}^2}}  = 20\,kg\,m{s^{ - 1}}.
\end{array}\)

\(\begin{array}{l}
The\,third\,piece\,has\,the\,same\,momentum\,\\
and\,in\,the\,direction\,opposite\,to\,the\,\\
{\rm{resultant}}\,of\,these\,two\,momenta.\\
\therefore \,Momentum\,of\,the\,third\,pices\\
 = 20\,kg\,m{s^{ - 1}}\\
\,\,\,\,\,Velocity\, = 4\,m{s^{ - 1}}\\
\therefore \,Mass\,of\,the\,{3^{rd}}piece\, = \frac{{mv}}{v} = \frac{{20}}{4} = 5kg
\end{array}\)