A particle moving with circumference |GravitationJEEMain2021

JEE MAIN 2021

26-02-2021 S1

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 $\mathrm{R}_3$. Its time period of revolution will be given by :

Select the correct option:

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

$T \propto R^{\frac{3}{2}}$

$T \propto R^{\frac{5}{2}}$

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

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

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

Question Tags

JEE Main

Physics

Easy

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