A) \[\sqrt{2({{u}^{2}}-gl)}\]
B) \[\sqrt{{{u}^{2}}-gl}\]
C) \[u-\sqrt{{{u}^{2}}-2gl}\]
D) \[\sqrt{2gl}\]
Correct Answer: A
Solution :
Using conservation of mechanical energy at initial and final position. \[\Delta K+\Delta U=0\] \[\left( \frac{1}{2}mu{{'}^{2}}-\frac{1}{2}m{{u}^{2}} \right)+(mgl)=0\] or \[u{{'}^{2}}={{u}^{2}}-2gl\] or \[u'=\sqrt{{{u}^{2}}-2gl}\] (i) So, the magnitude of change in velocity \[\Delta \vec{u}={{\vec{u}}_{f}}-{{\vec{u}}_{i}}={{\vec{u}}_{f}}+({{\vec{u}}_{i}})\] \[|\Delta \vec{u}|=\sqrt{u{{'}^{2}}+{{u}^{2}}}=\sqrt{({{u}^{2}}-2gh)+{{u}^{2}}}\] \[=\sqrt{2({{u}^{2}}-gl)}\]You need to login to perform this action.
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