A) \[\frac{{{v}^{2}}}{3\,g}\]
B) \[\frac{{{v}^{2}}}{4\,g}\]
C) \[\frac{{{v}^{2}}}{3\,g}\]
D) \[\frac{{{v}^{2}}}{6\,g}\]
E) \[\frac{{{v}^{2}}}{8\,g}\]
Correct Answer: E
Solution :
The collision is perfectly inelastic, hence the two balls sticks together. From conservation of energy, \[2mV=mv\] \[\Rightarrow \] \[V=\frac{v}{2}\] Now, from the principal of conservation of energy \[2mgh=\frac{1}{2}(2m)\,{{V}^{2}}\] \[=\frac{1}{2}(2m)\,{{\left( \frac{v}{2} \right)}^{2}}\] \[\Rightarrow \] \[h=\frac{{{v}^{2}}}{8g}\]You need to login to perform this action.
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