A) \[\frac{{{U}^{2}}}{8g}\]
B) \[\frac{{{U}^{2}}}{4g}\]
C) \[\frac{{{U}^{2}}}{2g}\]
D) \[\frac{{{U}^{2}}}{g}\]
Correct Answer: A
Solution :
Because the collision is perfectly inelastic, hence, the two blocks stick together. By conservation of linear momentum, 2 mV = mu or \[V=u/2,\]where V is the speed of the system after collision. By conservation of energy \[2mgh=\frac{1}{2}2m{{V}^{2}}\Rightarrow gh=\frac{1}{2}{{V}^{2}}\Rightarrow gh=\frac{1}{2}{{\left( \frac{u}{2} \right)}^{2}}\] \[\Rightarrow \,\,h=\frac{{{u}^{2}}}{8g}\] Hence, the correction option is [a].You need to login to perform this action.
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