A) \[\frac{b}{a}\]
B) \[\frac{a}{b}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{6}\]
Correct Answer: A
Solution :
Let any two points on the ellipse be \[{{c}_{2}}\] and \[{{c}_{1}}\] \[={{E}_{i}}\] \[={{E}_{f}}\] \[{{E}_{i}}=\frac{-GMm}{R}:\] \[{{E}^{f}}=-\frac{GMm}{2(2R+R)}\] \[[\because \,\,\text{height}\,=2R)\] \[={{E}_{f}}-{{E}_{i}}\] \[\Rightarrow \] \[\Delta E=\frac{-GMm}{6R}+\frac{GMm}{R}=\frac{5}{6}\,\frac{GMm}{R}\] \[\Rightarrow \] \[\Delta E=\frac{5}{6}\,mgR\] \[mg={{V}_{w}}{{\rho }_{w}}\,g+{{V}_{oil}}\,g\] \[{{V}_{w}}\] \[{{V}_{oil}}\] and \[{{\rho }_{w}}\] \[{{\rho }_{oil}}\] \[\Rightarrow \] Slope of \[m=(2\times 10\times 10\times 1)\,+(8\times 10\times 10\times 0.6)\] \[m=200+480=680\,g\]
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