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3-2.Motion in Plane
hard
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
A$T \propto R ^{2}$
B$T \propto R ^{\frac{3}{2}}$
C$T \propto R ^{\frac{5}{2}}$
D$T \propto R ^{\frac{4}{3}}$
(JEE MAIN-2021)
Solution
$F \propto \frac{1}{R^{3}}$
$\frac{K}{R^{3}}=m \omega^{2} R$
$\omega^{2}=\frac{K}{m} \times \frac{1}{R^{4}}$
$\left(\frac{2 \pi}{T}\right)^{2}=\frac{K}{m} \times \frac{1}{R^{4}}$
$T^{2} \propto R^{4}$
$T \propto R^{2}$
$\frac{K}{R^{3}}=m \omega^{2} R$
$\omega^{2}=\frac{K}{m} \times \frac{1}{R^{4}}$
$\left(\frac{2 \pi}{T}\right)^{2}=\frac{K}{m} \times \frac{1}{R^{4}}$
$T^{2} \propto R^{4}$
$T \propto R^{2}$
Standard 11
Physics
