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BITSAT 2010
Exam
BITSAT
Year
2010
Subject
Physics
Chapter
Gravitation

BITSAT 2010 · Physics · Gravitation

Suppose the gravitational force varies inversely as the nth power...

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius ' R\mathrm{R} ' around the sun will be proportional to

Options

  1. ARn\mathrm{R}^{\mathrm{n}}
  2. B\mathrm{R}^{\left(\frac{\mathrm{n}-1}{2}\right)}
  3. CR left(n+12)\mathrm{R} \ left(\frac{\mathrm{n}+1}{2})
  4. D\mathrm{R}^{\left(\frac{\mathrm{n}-2}{2}\right)}

Correct answer

C. R left(n+12)\mathrm{R} \ left(\frac{\mathrm{n}+1}{2})

Step-by-step solution

F=KR−n=MRω2⇒ω2=KR−(n+1)\mathrm{F}=\mathrm{KR}^{-\mathrm{n}}=\mathrm{MR} \omega^{2} \Rightarrow \omega^{2}=\mathrm{KR}^{-(\mathrm{n}+1)} or ω=K′R−(n+1)2\omega=\mathrm{K}^{\prime} \mathrm{R}^{\frac{-(\mathrm{n}+1)}{2}} [where K′=K1/2\mathrm{K}^{\prime}=\mathrm{K}^{1 / 2}, a constant ]2πTαR−(n+1)2∴TαR(n+1)2]\frac{2 \pi}{T} \alpha R^{\frac{-(n+1)}{2}} \quad \therefore T \alpha R^{\frac{(n+1)}{2}}
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