Question
The distance of Neptune and Saturn from the sun is nearly $${10^{13}}$$ and $${10^{12}}$$ meter respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio
A.
$$10$$
B.
$$100$$
C.
$$10\sqrt {10} $$
D.
$$1000$$
Answer :
$$10\sqrt {10} $$
Solution :
$$\eqalign{
& {T^2} \propto {R^3}\left( {{\text{According}}\,{\text{to}}\,{\text{Keple's}}\,{\text{law}}} \right) \cr
& T_1^2 \propto {\left( {{{10}^{13}}} \right)^3}\,\,{\text{and}}\,\,T_2^2 \propto {\left( {{{10}^{12}}} \right)^3} \cr
& \therefore \frac{{T_1^2}}{{T_2^2}} = {\left( {10} \right)^3}\,\,{\text{or}}\,\,\frac{{{T_1}}}{{{T_2}}} = 10\sqrt {10} \cr} $$