A) 2 months
B) 2 years
C) 2 days
D) 20 days
Correct Answer: A
Solution :
| When the Earth's motion is suddenly stopped, it would fall into the Sun and (suppose) it comes back. If the effect of temperature of Sun is ignored, we can say that the Earth would continue to move along a strongly extended flat ellipse whose extreme points are located at the Earth's orbit and at the centre of the Sun. |
| The semi major axis of such ellipse is \[R/2.\] |
| Now \[\frac{{{T}^{'2}}}{{{T}^{2}}}={{\left[ \frac{R}{2} \right]}^{3}}\left[ \frac{1}{{{R}^{3}}} \right]\] |
| Where 7'is the time period of normal orbit of |
| Earth, |
| Or \[T{{'}^{2}}=\frac{{{T}^{2}}}{8}\operatorname{or}\,T'=\frac{T}{2\sqrt{2}}\] |
| Now, time required to fall into the Sun, |
| \[t=\frac{T'}{2}=\frac{T}{4\sqrt{2}}=\frac{365}{4\sqrt{2}}\approx 65\operatorname{days}\] |
| So, the Earth would take slightly more than 2 months to fall into the Sun. |
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