A) \[d\sqrt{\frac{2{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}}\]
B) \[d\sqrt{\frac{2{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}}\]
C) \[=20m{{s}^{-1}}\]
D) \[(\text{take}\,g=10\text{ }m{{s}^{-}}^{2})\]
Correct Answer: C
Solution :
We have,\[x={{e}^{xy\frac{dy}{dx}}}\]\[\Rightarrow \]\[\log x=xy\frac{dy}{dx}\] \[\Rightarrow \]\[ydy=\frac{\log x}{x}dx\]\[\Rightarrow \]\[ydy=\log xd(\log x)\] On integrating both sides, we get \[\frac{{{y}^{2}}}{2}=\frac{{{({{\log }_{e}}x)}^{2}}}{2}+C\]\[\Rightarrow \]\[{{y}^{2}}={{({{\log }_{e}}x)}^{2}}+2C\] \[\Rightarrow \]\[y=\pm \sqrt{{{({{\log }_{e}}x)}^{2}}+2C}\]
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