Work Energy And Power Question 325
Question: 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?
Options:
A) $ 10\sqrt{2}m/s $
B) $ 15\sqrt{2}m/s $
C) $ 5\sqrt{2}m/s $
D) $ 20\sqrt{2}m/s $
Show Answer
Answer:
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=( 1/5x30 ) $
$ \therefore P=F.V=constant $
Resultant momentum
$ =\sqrt{{{{( 1/5 )\times 30}}^{2}}+{{{( 1/5 )\times 30}}^{2}}}=6\sqrt{2}kgm/\sec $
along the bisector of ÐAOB
$ ( 3/5 )\times v=6\sqrt{2}\Rightarrow v=10\sqrt{2}m/\sec $
