An explosive of mass M placed at a point explodes into one-third and two-third parts. If the initial kinetic energy of the smaller part is $1000 \; J$. What will be the initial kinetic energy of the bigger part?

Given,

Total mass = $M$

Mass of smaller fragment ($m_1 = $$\frac{1}{3}$$M$)

Mass of bigger fragment ($m_2 = $$\frac{2}{3}$$M$)

Kinetic Energy of smaller fragment ($E_1 = 1000\;J$)

Kinetic Energy of bigger fragment ($E_2 = \;?$)

We have,

$\frac{E_2}{E_1} = \frac{m_1}{m_2}$

$E_2 = $$\frac{m_1}{m_2}$$\;*\;E_1 = $$\frac{\frac{1}{3}M}{\frac{2}{3}M}$$\;*\;1000 = 500\;J$

∴ Initial kinetic energy of bigger fragment is $500\;J$

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