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  • 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  Option: 1</stron

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
 

Option: 1

\mathrm{\frac{1}{\sqrt{2}} \mathrm{~T}}
 


Option: 2

\mathrm{\frac{1}{2 \sqrt{2}} \mathrm{~T}}
 


Option: 3

\mathrm{\frac{1}{4 \sqrt{2}} \mathrm{~T}}
 


Option: 4

\mathrm{\frac{1}{8 \sqrt{2}} \mathrm{~T}}


Answers (1)

best_answer

The time \mathrm{ t_0} 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 ( \mathrm{ r} ).

\mathrm{\Rightarrow 2 \mathrm{a}=\mathrm{r}}

According to Kepler's Third Law,

\mathrm{\left(2 \mathrm{t}_0\right)^2 \propto \mathrm{a}^3 }

\mathrm{ \Rightarrow\left(2 \mathrm{t}_0\right)^2 \propto\left(\frac{\mathrm{r}}{2}\right)^3 }

Since, \mathrm{T^2 \propto r^3}

\mathrm{ \Rightarrow \frac{2 t_0}{T}=\frac{1}{\sqrt{8}} }

\mathrm{ \Rightarrow t_0=\frac{T}{4 \sqrt{2}} \frac{365}{4 \sqrt{2}}=64.53 \text { days } }

Hence option 3 is correct.




 

Posted by

Suraj Bhandari

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