An explosion blows a rock into three parts. Two parts go off at right angles of each other. These two are 1 kg first part moving with a velocity of 12ms−1 and 2 kg second part moving with a velocity of  8ms−1. If the third part files off with a velocity of 4ms−1, its mass would be :

[a] Apply law of conservation of linear momentum. Momentum of first part =1×12=12kgms−1. Momentum of the second part =2×8=16kgms−1.  Resultant momentum =(12)2+(16)2−−−−−−−−−−√=20kgms−1. The third part should also have the same momentum. Let the mass of the third part be M, then 4×M=20⇒M=5kg