A) \[m({{u}_{1}}-u_{2}^{2})\]
B) \[\frac{m}{4}{{({{u}_{1}}-{{u}_{2}})}^{2}}\]
C) \[\frac{m}{2}{{({{u}_{1}}-{{u}_{2}})}^{2}}\]
D) \[m{{({{u}_{1}}-{{u}_{2}})}^{3}}\]
Correct Answer: B
Solution :
Loss in kinetic energy \[=\frac{1}{2}\frac{{{m}_{1}}{{m}_{2}}{{({{u}_{1}}-{{u}_{2}})}^{2}}}{({{m}_{1}}+{{m}_{2}})}\] \[=\frac{1}{2}\frac{m\cdot m{{({{u}_{1}}-{{u}_{2}})}^{2}}}{(m+m)}\] \[=\frac{m}{4}{{({{u}_{1}}-{{u}_{2}})}^{2}}\]
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