A) 2 seconds
B) 3 seconds
C) 5 seconds
D) 6 seconds
Correct Answer: C
Solution :
Eccentricity of ellipse\[=\frac{1}{2}\] \[\Rightarrow \] \[\frac{de}{dt}=-0.1\] Eccentricity of auxiliary circle\[~=0\] \[\Rightarrow \] \[\int\limits_{1/2}^{0}{de=-0.1\int\limits_{0}^{T}{dt}}\] T is time at which it will touch the auxiliary circle. \[\Rightarrow \] \[-\frac{1}{2}=-0.1(T-0)\] \[\Rightarrow \]\[T=5\,\text{seconds}\text{.}\]
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