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 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.