Question

A particle is revolving in a circle of radius $R$. If the force acting on it is inversely proportional to $R$, then the time period is proportional to

• A. $R$
• B. $R^2$
• C. $I/R$
• D. $I/R^2$

Answer 1

Answer: (A)

$R$

Answer 2

Given that the force is inversely proportional to $R$ i.e. $F\,\mu\, \frac{1}{R}$ or$F = \frac{k}{R}... \left(i\right)$ or$mR \omega^{2} = \frac{k}{R}$ or$\omega^{2} = \frac{k}{mR^{2}}$ $\therefore \omega^{2}\mu \frac{1}{R^{2}}$ $\Rightarrow \omega\,\mu\, \frac{1}{R}$ $\Rightarrow \frac{2\pi}{T} \,\mu\, \frac{1}{R}$ $\Rightarrow T\,\mu\,R$