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Let $r$ be the radius of the orbot of the planet around the sun .

Let time taken to reach the sun be $'t'$ .

Time taken for the planet to revolve around the sun of radius $r=T$

We consider the planet to reach the sun is an elliptical path with time period $2t'=T'$

By Kepler's law

$\large\frac{T'}{T} =\bigg( \large\frac{r'}{r}\bigg)^{3/2}$

$r'= \large\frac{1}{2} $$r$

$T'= T\bigg(\large\frac{1}{2}\bigg)^{3/2}$

$t'= T\bigg(\large\frac{1}{2}\bigg)^{3/2}$$ \times \large\frac{1}{2}$

$t'=\large\frac{\sqrt 2}{8}$$T$

Hence b is the correct answer.

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