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Heisenberg's Uncertainty Principle

Two spheres o...

Question

Two spheres of masses $3 k g$ and $2 k g$ collide directly. Their relative velocity before collision is $15 m / s$ and after collision is $5 m / s$ . The total loss of $k . E .$ in joules due to collision is _____.

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Solution

Given : $m_{1} = 3 k g$ $m_{2} = 2 k g$ $u_{r e l} = 15 m / s$ $v_{r e l} = 5 m / s$
So, $e = \frac{v_{r e l}}{u_{r e l}} = \frac{5}{15} = \frac{1}{3}$
Loss in kinetic energy $Δ K . E = \frac{1}{2} (\frac{m_{1} m_{2}}{m_{1} + m_{2}}) (1 - e^{2}) (u_{r e l})^{2}$
Or $Δ K . E = \frac{1}{2} (\frac{3 \times 2}{3 + 2}) (1 - \frac{1}{3^{2}}) (15)^{2} = 120 J$

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