A stationary mass explodes into two parts of mass $4 \; kg$ and $40 \; kg$. The initial kinetic energy of larger mass is $10 \; J$. What is the initial kinetic energy of the smaller mass and its velocity.

Given,

Mass ($M_1) = 4\;kg$

Mass ($M_2) = 40\;kg$

Initial kinetic energy of larger mass $(E_2) = 10\;J$

Initial kinetic energy of the smaller mass $(E_1) = \;?$

Velocity of the smaller part $(V_1) = \;?$

We have,

$\frac{E_1}{E_2} = \frac{M_2}{M_1}$

$E_1 = $$\frac{E_2\;*\;M_2}{M_1}$$ = \frac{10 \;*\; 40}{4}$$ = 100\;J$

Now to calculate the velocity of the smaller part,

$E_1 = \frac{1}{2}\;M_1\;V_1^2$

$V_1^2 = \frac{2\;*\;E_1}{M_1}$

⇒ $V_1 = \sqrt{\frac{2\;*\;E_1}{M_1}} = \sqrt{\frac{2\;*\;100}{4}} = 7.07\;m/s  $

∴ Initial kinetic energy of the smaller mass $(E_1) = \;100\;J$

∴ Velocity of the smaller part $(V_1) = \;7.07\;m/s$

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