Answer:
Mass of a
cracker,\[m=100g=\frac{100}{1000}kg=0.1kg\]
Initially, cracker
is at rest i.e., u = 0
Therefore,
initial momentum of the cracker = mu = 0
After
explosion, mass of each piece
\[=\frac{0.1}{2}kg=0.05kg\]
\[\therefore \]\[{{m}_{1}}=0.05kg\]and\[{{m}_{2}}=0.05kg\]
Let, \[{{\upsilon
}_{1}}=\]velocity of first piece
\[{{\upsilon
}_{2}}=\] velocity of second piece
\[\therefore
\]Momentum of cracker after explosion
\[={{m}_{1}}{{\upsilon
}_{1}}+{{m}_{2}}{{\upsilon }_{2}}\]
\[=0.05{{\upsilon
}_{1}}+0.05{{\upsilon }_{2}}\]
Applying law
of conservation of momentum Total final momentum = Total initial momentum\[0.05{{\upsilon
}_{1}}+0.05{{\upsilon }_{2}}=0\]or
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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