Question

If the earth is one-fourth of its present distance from the sun, the duration of the year will be changed to

• A. half of the present year
• B. $(\frac{1^{th}}{4})$ of the present year
• C. $(\frac{1^{th}}{8})$ of the present year
• D. $(\frac{7^{th}}{8})$ of the present year
• E. $(\frac{1^{th}}{16})$ of the present year

Answer 1

Answer: (C)

From Kepler's law,
$ T^{2} \propto r^{3} $
Hence, $\left(\frac{T_{1}}{T_{2}}\right)^{2} =\left(\frac{r_{1}}{r_{2}}\right)^{3}=\left(\frac{r}{r / 4}\right)^{3} $
$ \frac{T_{1}}{T_{2}} =(4)^{3 / 2} $
$ T_{2} =\frac{T_{1}}{4^{3 / 2}} $
$T_{2} =\frac{T_{1}}{8} $