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STD 11 - 7. gravitation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 7. gravitation4 Marks
MCQ
An artificial satellite revolves around a planet for which gravitational force $(F)$ varies with distance $r$ from its centre as $F \propto r^2$. If $v_0$ its orbital speed, then
  • A
    $v_0 \propto r^{-1 / 2}$
  • ✓
    $v_0 \propto r^{3 / 2}$
  • C
    $v_0 \propto r^{-3 / 2}$
  • D
    $v_0 \propto r$
✓

Answer

Correct option: B.
$v_0 \propto r^{3 / 2}$
b
(b)

Gravitational force $(F)$ provides the necessary centripetal force to keep the satellite in orbit,

$\Rightarrow \frac{m v_0^2}{r} \propto F$

$\frac{m v_0^2}{r} \propto r^2$

$v_0 \rightarrow \text { Orbital speed }$

$r \rightarrow \text { Radius of orbit }$

$\Rightarrow v_0 \propto r^{3 / 2}$

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