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7.Gravitation
normal
Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
A
${R^{\left( {\frac{{n + 1}}{2}} \right)}}$
B
${R^{\left( {\frac{{n - 1}}{2}} \right)}}$
C
${R^n}$
D
${R^{\left( {\frac{{n - 2}}{2}} \right)}}$
Solution
Force $\propto \frac{1}{R^{n}}$
$\mathrm{MR} \omega^{2} \propto \mathrm{R}^{-\mathrm{n}}$
$\Rightarrow \omega \propto_{R} \frac{(n+1)}{2} \Rightarrow T \propto R^{\frac{(n+1)}{2}}$
Standard 11
Physics
