Question

A body of mass M kg initially at rest explodes into three fragments having masses in the ratio $3:1:1$ . The two equal mass fragments fly off at right angles to each other with equal speed of 60 m/s. The speed of the heavier fragment is

• A. $30\sqrt{2}\,m/s$
• B. $10\sqrt{2}\,m/s$
• C. $20\sqrt{2}\,m/s$
• D. $20\,m/s$

Answer 1

Answer: (C)

$20\sqrt{2}\,m/s$

Answer 2

: Momentum is conserved $\therefore$ (3mv) = Momentum of heavy particle $\therefore$ $mu=$ momentum of lighter particle ${{(mu)}^{2}}+{{(mu)}^{2}}={{(3mv)}^{2}}$ or $2{{m}^{2}}{{u}^{2}}=9{{m}^{2}}{{v}^{2}}\Rightarrow 2\times {{(60)}^{2}}=9{{r}^{2}}$ or ${{v}^{2}}=\frac{2\times 60\times 60}{9}=2\times 400$ or $v=20\sqrt{2}m/s$