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COE in Elastic Collision

Two perfectly...

Question

Two perfectly elastic balls of the same mass $m$ are moving with velocities $u_{1}$ and $u_{2}$ . They collide head on elastically, $n$ times. The kinetic energy of the sytem finally is

\frac{1}{2} \frac{m}{n} u_{1}^{2}

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\frac{1}{2} \frac{m}{n} (u_{1}^{2} + u_{2}^{2})

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

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\frac{1}{2} m n (u_{1}^{2} + u_{2}^{2})

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Solution

The correct option is C $\frac{1}{2} m (u_{1}^{2} + u_{2}^{2})$
As we know,
In elastic collision kinetic energy of the system remains same before and after the collision.
Hence after the collision, $K E$ will be same as the initial kinetic energy before the collision.
Therefore, kinetic energy after $n$ collisions $= \frac{1}{2} m u_{1}^{2} + \frac{1}{2} m u_{2}^{2} = \frac{1}{2} m (u_{1}^{2} + u_{2}^{2})$

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COE in Elastic Collision

Standard XI Physics

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Two perfectly elastic balls of the same mass m are moving with velocities u1 and u2. They collide head on elastically, n times. The kinetic energy of the sytem finally is

Two perfectly elastic balls of the same mass $m$ are moving with velocities $u_{1}$ and $u_{2}$ . They collide head on elastically, $n$ times. The kinetic energy of the sytem finally is