Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet…

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet in circular orbit of radius $\mathrm{R}$ around the sun will be proportional to
  1. $R^{\left(\frac{n+1}{2}\right)}$
  2. $R^{\left(\frac{n-1}{2}\right)}$
  3. $\mathrm{R}^{\mathrm{n}}$
  4. $\mathrm{R}^{\left(\frac{\mathrm{n}-2}{2}\right)}$

Solution

$\mathrm{T} \propto \mathrm{R}^{(\mathrm{n}+1) / 2}$

Asked in: JEE Main 2004

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