A) \[k/n\]
B) \[\frac{\left( n-1 \right)k}{n}\]
C) \[\frac{\left( n+1 \right)k}{n}\]
D) \[\frac{nk}{\left( n+1 \right)}\]
Correct Answer: D
Solution :
| Given, \[k=\frac{1}{2}m{{v}^{2}}\] |
| If \[v'\] is the velocity of the balls during collision, then |
| \[mv+0=(m+nm){v}'\,\,\,\,\,\,;\,\,\,\,\,\,\,\,v'=\left( \frac{v}{n+1} \right)\] |
| The maximum potential energy stored during collision, |
| \[=\frac{1}{2}m{{v}^{2}}-\frac{1}{2}\left( m+nm \right)v{{'}^{2}}\] |
| \[=\frac{1}{2}m{{v}^{2}}-\frac{1}{2}\left( n+1 \right)\frac{m{{v}^{2}}}{{{\left( n+1 \right)}^{2}}}\] |
| \[=k-\frac{k}{n+1}=\frac{nk}{n+1}\] |
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