A) \[{{m}_{1}}u_{1}^{2}+{{m}_{2}}u_{2}^{2}-\varepsilon ={{m}_{1}}\upsilon _{1}^{2}+{{m}_{2}}\upsilon _{2}^{2}\]
B) \[\frac{1}{2}{{m}_{1}}u_{1}^{2}+\frac{1}{2}{{m}_{2}}u_{2}^{2}=\frac{1}{2}{{m}_{1}}u_{1}^{2}\]\[+\frac{1}{2}{{m}_{2}}u_{2}^{2}-\varepsilon \]
C) \[\frac{1}{2}{{m}_{1}}u_{1}^{2}+\frac{1}{2}{{m}_{2}}u_{2}^{2}-\varepsilon =\frac{1}{2}{{m}_{1}}u_{1}^{2}\]\[+\frac{1}{2}{{m}_{2}}u_{2}^{2}\]
D) \[\frac{1}{2}m_{1}^{2}u_{1}^{2}+\frac{1}{2}m_{2}^{2}u_{2}^{2}+\varepsilon =\frac{1}{2}m_{1}^{2}u_{1}^{2}\]\[+\frac{1}{2}m_{2}^{2}u_{2}^{2}\]
Correct Answer: C
Solution :
\[K{{E}_{Before\,cellision}}=\frac{1}{2}{{m}_{1}}u_{1}^{2}+\frac{1}{2}{{m}_{2}}u_{2}^{2}\] \[K{{E}_{After\,cellision}}=\frac{1}{2}{{m}_{1}}u_{1}^{2}+\frac{1}{2}{{m}_{2}}u_{2}^{2}\] \[=\frac{1}{2}{{m}_{1}}u_{1}^{2}+\frac{1}{2}{{m}_{2}}u_{2}^{2}-\varepsilon \] \[K{{E}_{Before\,collision}}=K{{E}_{After\,collision}}\] \[=\frac{1}{2}{{m}_{1}}u_{1}^{2}+\frac{1}{2}{{m}_{2}}u_{2}^{2}-\varepsilon =\frac{1}{2}{{m}_{1}}u_{1}^{2}+\frac{1}{2}{{m}_{2}}u_{2}^{2}\]You need to login to perform this action.
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