A) \[\sqrt{\frac{2b}{a}}\]
B) \[\sqrt{\frac{A}{2b}}\]
C) \[\sqrt{\frac{a}{b}}\]
D) \[\sqrt{\frac{b}{a}}\]
E) \[\sqrt{ba}\]
Correct Answer: B
Solution :
\[y=b{{x}^{2}}\] \[\frac{dy}{dt}=2bx\frac{dx}{dt}\] ...(i) \[\frac{dy}{dt}=at\] \[(\because {{v}_{y}}={{u}_{y}}+{{a}_{y}}t)\] \[at=2bx\frac{dx}{dt}\] \[atdt=2bx\,dx\] Take integration of both sides \[\int{atdt}=\int{2bx}\,dx\] \[\frac{a{{t}^{2}}}{2}=b{{x}^{2}}+c\] ...(ii) At \[t=0,\text{ }x=0\] \[c\Rightarrow 0\] Then, \[\frac{a{{t}^{2}}}{2}=b{{x}^{2}}\] \[x=\sqrt{\frac{a{{t}^{2}}}{2b}}=t\sqrt{\frac{a}{2b}}\] \[\therefore \] \[{{v}_{x}}=\frac{dx}{dt}=\sqrt{\frac{a}{2b}}\]
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