question_answer

A cracker of mass 100 g explodes into two pieces of equal mass. Show that these two pieces of the cracker fly in opposite direction.

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.