If the earth suddenly stopped in its orbit (assume orbit to be circular) the time that would elapse before it falls into the sun is
Answer & explanation
Correct answer: option 3
The time t0 taken by earth to fall into the sun can be calculated by considering a very elongated ellipse having major axis equal to the radius of orbit of earth about sun (r).
⇒ 2a = r
According to Kepler's Third Law,
$\left(2 t_0\right)^2 \propto a^3$
$\Rightarrow\left(2 t_0\right)^2 \propto\left(\frac{r}{2}\right)^3$
Since, $T^2 \propto r^3$
$\Rightarrow \frac{2 t_0}{T}=\frac{1}{\sqrt{8}}$
$\Rightarrow t_0=\frac{T}{4 \sqrt{2}} \frac{365}{4 \sqrt{2}}$ = 64.53 days