Answer:
Mass of
cracker ;\[m=100g=\frac{100}{1000}kg=0.1kg\]
Initially cracker is
at rest, u = 0
\[\therefore
\] Initial momentum of the cracker = mu =0
After
explosion, mass of each piece \[=\frac{0.1}{2}=0.05kg\]
\[\therefore \]\[{{m}_{1}}={{m}_{2}}=0.05kg\]
Let \[{{\upsilon
}_{1}}=\]velocity of first piece
and \[{{\upsilon
}_{2}}=\]velocity of second piece
\[\therefore \] Momentum of cracker
after explosion
\[={{m}_{1}}{{\upsilon
}_{1}}+{{m}_{2}}{{\upsilon }_{2}}\]
\[=0.05\,{{\upsilon
}_{1}}+0.05{{\upsilon }_{2}}\]
According to
law of conservation momentum,
\[{{m}_{1}}{{\upsilon
}_{1}}+{{m}_{2}}{{\upsilon }_{2}}=mu\]
\[\Rightarrow
0.05{{\upsilon }_{1}}+0.05{{\upsilon }_{2}}=0\]
\[\Rightarrow
{{\upsilon }_{1}}=-{{\upsilon }_{2}}\]
The negative
sign shows that \[{{\upsilon }_{1}}\] and \[{{\upsilon }_{2}}\] are equal in magnitude
and opposite in direction.
Thus, two pieces of
the cracker fly in opposite directions with same speed.
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