Question

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

• A. $10m/s$
• B. $20m/s$
• C. $10\sqrt{2}m/s$
• D. $20\sqrt{2}m/s$

Answer 1

The correct option is C $10\sqrt{2}m/s$

The masses of all three-part are 200g, 200g, and 600g.

Now the momentum of two particle is $P_1=200\times {10}^{-3}\times 30=6kg.m/s$

$P_2=200\times {10}^{-3}\times 30=6kg.m/s$

Since they are perpendicular to each other, so $P^2=P_1^2+P_2^2$

The momentum of the heavy particles should be opposite and equal to $P$ from the conservation of linear momentum.

So $600\times {10}^{-3}\times V=\sqrt{(6{)}^2+(6{)}^2}$

$V=10\sqrt{2}m/s$