Question

If the earth is at one-fourth of its present distance from the sun, the duration of the year would be:

• A. Half the present year
• B. One-eighth the present year
• C. One-fourth the present year
• D. One -sixteenth the present year

Answer 1

Answer: (B)

One-eighth the present year

Relationship of time period of a satellite to the radius is given by:
$T^2\propto R^3$
$\Rightarrow {\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{R_1}{R_2}\right)}^3$
$\Rightarrow T_2=T_1{\left(\frac{R_2}{R_1}\right)}^{3/2}=T_1{\left(\frac{R_1/4}{R_1}\right)}^{3/2}=\frac{T_1}{8}$