A ball of mass $m$ at rest receives an impulse $I_{1}$ in the direction of north. After some time, it received another impulse $I_{2}$ in the direction of south. The final kinetic energy of the ball is

\frac{(I_{1} + I_{2})^{2}}{2 m}

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\frac{(I_{1} - I_{2})^{2}}{2 m}

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\frac{I_{1}^{2} + I_{2}^{2}}{2 m}

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\frac{I_{1}^{2} - I_{2}^{2}}{2 m}

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Solution

The correct option is D $\frac{(I_{1} - I_{2})^{2}}{2 m}$
Change in momentum, $Δ P = I_{2} - I_{1}$

$Δ K E = \frac{Δ P^{2}}{2 m} = \frac{(I_{1} - I_{2})^{2}}{2 m}$

where $I_{1}$ and $I_{2}$ are vectors.

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