A) \[\frac{h}{3},\,\frac{\sqrt{2gh}}{3}\]
B) \[\frac{h}{3},\,\frac{\sqrt{gh}}{3}\]
C) \[\frac{2h}{3},\,\frac{\sqrt{2gh}}{3}\]
D) \[\frac{h}{3},\,\sqrt{2gh}\]
Correct Answer: B
Solution :
| [b] Total mechanical energy = mgh |
| As, \[\frac{KE}{PE}=\frac{2}{1}\] |
| \[\frac{KE}{PE}=\frac{2}{1}\] mgh and \[PE=\frac{1}{3}mgh\] |
| Height from the ground at this instant, |
| \[h'=\frac{h}{3},\] and speed of particle at this instant, |
| \[v=\sqrt{2g(h-h')}=\sqrt{2g\left( \frac{2h}{3} \right)}=2\sqrt{\frac{gh}{3}}\] |
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