A) 3 m/s
B) 2.5 m/s
C) 2.0 m/s
D) 1.5 m/s
Correct Answer: B
Solution :
Key Idea: Momentum of system remain conserved in universe. From law of conservation of momentum the total momentum of the system is conserved. Given, mass of body is M, mass of two particles \[\frac{M}{4}\times 2=\frac{M}{2}\] Hence, mass of third piece is\[\frac{M}{2}.\] Also since particles are thrown off in perpendicular directions, vector sum of the momentum of the first two pieces is numerically equal but opposite in direction to the momentum of third piece. \[v\left( \frac{M}{2} \right)=\sqrt{{{\left( \frac{3M}{4} \right)}^{2}}+{{\left( \frac{4M}{4} \right)}^{2}}}\] \[\Rightarrow \] \[v=2.5\,m/s\]
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