Question

If the distance of earth from the sun reduces to one fourth of its present value then the length of the year will become

• A. $1/6$ of present year
• B. $1/8$ of present year
• C. $1/4$ of present year
• D. $1/2$ of present year

Answer 1

The correct option is B $1/8$ of present year

According to Kepler's law, $T\propto (r{)}^{\frac{3}{2}}$
$\frac{T_1}{T_2}={\left(\frac{r_1}{r_2}\right)}^{\frac{3}{2}}$
$T_2=T_1{\left(\frac{r_2}{r_1}\right)}^{\frac{3}{2}}=T_1{\left(\frac{1}{4}\right)}^{\frac{3}{2}}=\frac{T_1}{8}$
Length of year will become $1/8$ of present year.