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7. gravitation — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics7. gravitation1 Mark
MCQ
A light planet is revolving around a massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the force of attraction between planet and star is proportional to $\mathrm{R}^{-3 / 2}$ then choose the correct option :
  • ✓
    $\mathrm{T}^2 \propto \mathrm{R}^{5 / 2}$
  • B
    $T^2 \propto R^{7 / 2}$
  • C
    $T^2 \propto R^{3 / 2}$
  • D
    $T^2 \propto R^3$
✓

Answer

Correct option: A.
$\mathrm{T}^2 \propto \mathrm{R}^{5 / 2}$
a
$\mathrm{F}=\frac{\mathrm{GMm}}{\mathrm{R}^{3 / 2}}=\mathrm{m} \omega^2 \mathrm{R}$

$\omega^2 \propto \frac{1}{\mathrm{R}^{5 / 2}} \quad \because \mathrm{T}=\frac{2 \pi}{\omega} \quad \text { so }$

$\mathrm{T}^2 \propto \mathrm{R}^{5 / 2}$

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