A) \[\frac{16}{25}\]
B) \[\frac{2}{5}\]
C) \[\frac{3}{5}\]
D) \[\frac{9}{25}\]
Correct Answer: B
Solution :
[b] According to principle of conservation of energy Potential energy = kinetic energy \[\Rightarrow mgh =\frac{1}{2}m{{v}^{2}}\Rightarrow v =\sqrt{2gh}\] If \[{{\operatorname{h}}_{1}} and {{h}_{2}}\]are initial and final heights, then \[\Rightarrow {{v}_{1}}=\sqrt{2g{{h}_{1}}},{{v}_{2}}=\sqrt{2g{{h}_{2}}}\] Loss in velocity, \[\Delta v={{v}_{1}}-{{v}_{2}}=\sqrt{2g{{h}_{1}}}-\sqrt{2g{{h}_{2}}}\] \[\therefore \]fractional loss in velocity \[=\frac{\Delta v}{{{v}_{1}}}=\frac{\sqrt{2g{{h}_{1}}}-\sqrt{2g{{h}_{2}}}}{\sqrt{2g{{h}_{1}}}}=1-\frac{{{h}_{2}}}{{{h}_{1}}}\] \[=1-\sqrt{\frac{1.8}{5}}=1-\sqrt{0.36}=1-0.6=0.4=\frac{2}{5}\]
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