Two planets revolve round the sun with frequencies N_1 and N_2 re… - Vidyadip

MCQ

Two planets revolve round the sun with frequencies ${N_1}$ and ${N_2}$ revolutions per year. If their average orbital radii be ${R_1}$ and ${R_2}$ respectively, then ${R_1}/{R_2}$ is equal to

A
${({N_1}/{N_2})^{3/2}}$
B
${({N_2}/{N_1})^{3/2}}$
C
${({N_1}/{N_2})^{2/3}}$
✓
${({N_2}/{N_1})^{2/3}}$

✓

Answer

Correct option: D.

${({N_2}/{N_1})^{2/3}}$

d
(d) According to Kepler's law ${T^2} \propto {R^3}$

If $N$ is the frequencs then ${N^2} \propto {(R)^{ - 3}}$

or $\frac{{{N_2}}}{{{N_1}}} = {\left( {\frac{{{R_2}}}{{{R_1}}}} \right)^{ - 3/2}}$==> $\frac{{{R_1}}}{{{R_2}}} = {\left( {\frac{{{N_2}}}{{{N_1}}}} \right)^{2/3}}$

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