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.