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7.Gravitation
medium
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
${({N_1}/{N_2})^{2/3}}$
D
${({N_2}/{N_1})^{2/3}}$
Solution
(d) According to Kepler's law ${T^2} \propto {R^3}$
If $N$ is the frequencs then ${N^2} \propto {(R)^{ – 3}}$
or $\frac{{{N_2}}}{{{N_1}}} = {\left( {\frac{{{R_2}}}{{{R_1}}}} \right)^{ – 3/2}}$==> $\frac{{{R_1}}}{{{R_2}}} = {\left( {\frac{{{N_2}}}{{{N_1}}}} \right)^{2/3}}$
Standard 11
Physics
Similar Questions
Match List$-I$ With List$-II$
| $(a)$ Gravitational constant $(G)$ | $(i)$ $\left[ L ^{2} T ^{-2}\right]$ |
| $(b)$ Gravitational potential energy | $(ii)$ $\left[ M ^{-1} L ^{3} T ^{-2}\right]$ |
| $(c)$ Gravitational potential | $(iii)$ $\left[ LT ^{-2}\right]$ |
| $(d)$ Gravitational intensity | $(iv)$ $\left[ ML ^{2} T ^{-2}\right]$ |
Choose the correct answer from the options given below:
