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3.2 , motion in plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics3.2 , motion in plane1 Mark
MCQ
A particle is moving with uniform speed along the circumference of a circle of radius $R$ under the action of a central fictitious force $F$ which is inversely proportional to $R ^{3}$. Its time period of revolution will be given by
  • ✓
    $T \propto R ^{2}$
  • B
    $T \propto R ^{\frac{3}{2}}$
  • C
    $T \propto R ^{\frac{5}{2}}$
  • D
    $T \propto R ^{\frac{4}{3}}$
✓

Answer

Correct option: A.
$T \propto R ^{2}$
a
$F \propto \frac{1}{R^{3}}$

$\frac{K}{R^{3}}=m \omega^{2} R$

$\omega^{2}=\frac{K}{m} \times \frac{1}{R^{4}}$

$\left(\frac{2 \pi}{T}\right)^{2}=\frac{K}{m} \times \frac{1}{R^{4}}$

$T^{2} \propto R^{4}$

$T \propto R^{2}$

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