Question

A bomb of mass 1 kg initially at rest explodes and breaks into three segments of masses in the ratio 1:1:3. The two pieces of equal masses fly off perpendicular to each other with a speed 15 m/s each. The speed of heavier segment is

1. 5 m/s b) 15 m/s c) 45 m/s d) 5*root 2 m/s

Answer 1

$$\begin{gathered} Initialmomentumofthesystemisgivenby: \\ P=Mv=0 \\ M=m+m+3m=4m \\ momentumofthetwoparticleshavingsamemassisggivenby: \\ {P}_1=mv=15m \\ {P}_1=mv=15m \\ fortheconsevrationoflinearmomentum, \\ finalmomentum=initialmomentum \\ finalmomentummustbeequalotzero. \\ therefore\text{'}momentumofthethirdparticlewillsameastheresultantmomentumofthetwoparticlesbutinoppositedirection. \\ {P}_3=\sqrt{{P_1}^2+{P_2}^2}=\sqrt{225m^2+225m^2}=15m\sqrt{2} \\ {P}_3=2m{v}_3 \\ {v}_3=\frac{15m\sqrt{2}}{2m}=5.204m/s \end{gathered}$$