question_answer

A body of mass 1 kg initially at rest explodes and breaks into three fragments of masses in the ratio 1 : 1 : 3. The two pieces of equal mass fly off perpendicular to each other with a speed of 30 m/sec each. What is the velocity of the heavier fragment?

A) \[10\sqrt{2}\,m/s\]

B) \[15\sqrt{2}\,m/s\]

C) \[5\sqrt{2}\,\,m/s\]

D)  \[20\sqrt{2}\,\,m/s\]

Correct Answer: A

Solution :

[a] The situation is shown in fig.

Let A and B be two pieces of equal mass (1/5 kg) which fly off perpendicular to a each other with equal velocity (30m/sec)

Momentum of A or \[\sqrt{3}B=\left( 1/5\text{ }x\text{ }30 \right)\]

\[\therefore P=F.V=constant\] Resultant momentum

\[=\sqrt{{{\{\left( 1/5 \right)\times 30\}}^{2}}+{{\{\left( 1/5 \right)\times 30\}}^{2}}}=6\sqrt{2}\,kg\,m/\sec \]

along the bisector of ÐAOB

\[\left( 3/5 \right)\times v=6\sqrt{2}\Rightarrow v=10\sqrt{2}m/\sec \]