A) \[4\text{ }h\]
B) \[2\text{ }s\]
C) \[1/\sqrt{2}s\]
D) \[\sqrt{2}s\]
Correct Answer: A
Solution :
Here, initial velocity of the body \[{{v}_{1}}=v\] Initial height \[h=hc\] Final velocity of the body \[{{v}^{2}}=2v\] Now, from the equation of motion \[{{v}^{2}}={{u}^{2}}+2gh\] \[{{v}^{2}}\propto h\] So, \[{{\left[ \frac{{{v}_{1}}}{{{v}_{2}}} \right]}^{2}}=\left[ \frac{{{h}_{1}}}{{{h}_{2}}} \right]\] Or, \[{{\left[ \frac{v}{2v} \right]}^{2}}=\frac{h}{{{h}_{2}}}\] Or, \[\frac{h}{{{h}_{2}}}=\frac{1}{4}\] Or, \[{{h}_{2}}=4h\]
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