A) The kinetic energy of the A-B system at maximum compression of the spring is zero
B) The kinetic energy of the A-B system at maximum compression of the spring is \[m{{v}^{2}}/4\]
C) The maximum compression of the spring is \[v\sqrt{m/K}\]
D) The maximum compression of the spring is \[v\sqrt{m/2K}\]
Correct Answer: B
Solution :
Let the velocity acquired by A and B be V, then \[mv=mV+mV\Rightarrow V=\frac{v}{2}\] Also \[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m{{V}^{2}}+\frac{1}{2}m{{V}^{2}}+\frac{1}{2}k{{x}^{2}}\] Where x is the maximum compression of the spring. On solving the above equations, we get \[x=v{{\left( \frac{m}{2k} \right)}^{1/2}}\] At maximum compression, kinetic energy of the A ? B system \[=\frac{1}{2}m{{V}^{2}}+\frac{1}{2}m{{V}^{2}}=m{{V}^{2}}=\frac{m{{v}^{2}}}{4}\]
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