Question

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. $T \propto R ^{\frac{4}{3}}$

Answer 1

Answer: (A)

$F \propto \frac{1}{R^{3}}$
$\frac{K}{R^{3}}=m \omega^{2} R$
$\omega^{2}=\frac{K}{m} \times \frac{1}{R^{4}}$
$\left(\frac{2 \pi}{T}\right)^{2}=\frac{K}{m} \times \frac{1}{R^{4}}$
$T^{2} \propto R^{4}$
$T \propto R^{2}$